IGCSE Physics · Area 1 · Motion, Forces and Energy

Motion

Motion is the study of how objects move: speed, velocity and acceleration, and the graphs that describe them. This topic covers the equations for speed and acceleration, how to read distance-time and speed-time graphs, and why a falling object reaches terminal velocity.

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Syllabus coverage

  • Define speed as distance travelled per unit time, and recall and use the equation v = s / t
  • Define velocity as speed in a given direction
  • Recall and use the equation average speed = total distance travelled / total time taken
  • Sketch, plot and interpret distance-time and speed-time graphs
  • Determine, qualitatively, from given data or the shape of a distance-time or speed-time graph when an object is at rest, moving with constant speed, accelerating or decelerating
  • Calculate speed from the gradient of a straight-line section of a distance-time graph
  • Calculate the area under a speed-time graph to determine the distance travelled for motion with constant speed or constant acceleration
  • State that the acceleration of free fall g for an object near to the surface of the Earth is approximately constant and is approximately 9.8 m/s2
  • Define acceleration as change in velocity per unit time, and recall and use the equation a = (v - u) / t
  • Determine from given data or the shape of a speed-time graph when an object is moving with constant acceleration or with changing acceleration
  • Calculate acceleration from the gradient of a speed-time graph
  • Know that a deceleration is a negative acceleration and use this in calculations
  • Describe the motion of objects falling in a uniform gravitational field with and without air or liquid resistance, including reference to terminal velocity

Part of the IGCSE Physics syllabus 0625.

A velocity-time graphThe gradient is the acceleration. The area between the line and the time axis is the distance travelled.0246805101520Time (s)Velocity(m/s)area = distance travelled3 s x 12 m/s = 36 mconstant velocity 12 m/sacceleration is zeroacceleratinggradient = accelerationdeceleratinggradient = -4.0 m/s2Rising lineVelocity increases, so theacceleration is positive.Horizontal lineVelocity is constant, so theacceleration is zero.Falling lineVelocity decreases, so theobject is decelerating.Area under the lineDistance travelled. Split itinto a rectangle and a triangle.Reading the graphAcceleration = gradient = change in velocity / change in time. From 0 s to 2 s the velocityrises 12 m/s in 2 s, so a = 12 / 2 = 6.0 m/s2. From 2 s to 5 s the line is horizontal, so a = 0.Distance = area under the line. The shaded rectangle is 3 s x 12 m/s = 36 m.
A speed-time graph for a vehicle: a straight sloping line shows constant acceleration, a horizontal line shows constant speed, and a line falling back to zero shows constant deceleration. The gradient of each section gives the acceleration, and the area under the whole graph gives the distance travelled.

Speed: distance travelled per unit time

Speed is the distance an object travels in each unit of time. If a car covers 100 metres every second, its speed is 100 m/s. The equation is speed = distance travelled / time taken, usually written v = s / t, where v is the speed in metres per second (m/s), s is the distance in metres (m) and t is the time in seconds (s).

The unit of speed comes straight from the equation: metres divided by seconds gives m/s. You will also meet km/h and miles per hour. To change km/h into m/s, multiply by 1000 and divide by 3600, which is the same as dividing by 3.6. So 72 km/h is 72 / 3.6 = 20 m/s.

Put numbers in carefully and the marks follow. A cyclist travels 1500 m in 120 s: v = s / t = 1500 / 120 = 12.5 m/s. Write the equation, then the substitution, then the answer with its unit; examiners usually split the marks that way.

Real journeys rarely happen at one steady speed. If a bus keeps stopping and starting, the speed you work out with v = s / t is the average speed - the single steady speed that would cover the same total distance in the same total time. For a journey in stages, add up all the distances and all the times first, then use average speed = total distance travelled / total time taken.

Speed is how fast distance is covered, so it is always a distance divided by a time and always carries the unit m/s.
A roadside speed camera timing a car over a measured stretch of road, an everyday use of speed = distance / time.

Speed and velocity: direction matters

Velocity is speed in a given direction. Two cars can both be travelling at 20 m/s, but if one is heading north and the other south they have the same speed and opposite velocities. A quantity with a direction, such as velocity, is called a vector; a quantity with size only, such as speed or distance, is called a scalar.

Direction matters because a change in velocity includes a change in direction, even when the speed is constant. A car going round a roundabout at a steady 10 m/s is accelerating, because its direction - and so its velocity - is changing. Remember that acceleration means any change in velocity, not just getting faster.

Velocity is measured in the same unit as speed, m/s, and you use the same equation, v = s / t, but you must state the direction as well. An answer of '20 m/s' is a speed; '20 m/s due east' is a velocity.

Speed has size only; velocity has size and direction. If a question asks for the velocity, the direction is part of the answer.

Distance-time graphs: the gradient is the speed

A distance-time graph has distance on the vertical axis and time on the horizontal axis. The shape of the line tells you what the object is doing, and the gradient (slope) of the line is the speed. A steeper line means a greater speed.

To calculate a speed, pick a straight section and read the change in distance and the change in time across it. On a graph that rises from 0 m at 0 s to 40 m at 8 s, the gradient is 40 / 8 = 5.0 m/s.

Watch the axes. The gradient is the change in the vertical value divided by the change in the horizontal value, so on a distance-time graph it is distance / time and the unit is m/s. Dividing the wrong way round gives seconds per metre, which is a sure sign the calculation has been turned upside down.

  • Horizontal line: the object is at rest, because the distance is not changing.
  • Straight sloping line: constant speed, and a steeper slope is a greater speed.
  • Curve getting steeper: the object is speeding up (accelerating).
  • Curve flattening out: the object is slowing down (decelerating).
A distance-time graphThe gradient of a distance-time graph is the speed. A horizontal section means the object is stationary.02468020406080Time (s)Distance(m)steady speed10 m/sstationaryat 20 msteeper, 15 m/sreturn to zero-25 m/sgradient = speedSloping lineSteady speed. The steeper theline, the greater the speed.Horizontal lineThe distance does not change, sothe speed is zero.CurveThe speed is changing. Steepermeans accelerating.Line back to zeroThe object returns to thestarting point.Reading the graphSpeed = gradient = change in distance / change in time. From 0 s to 2 s the line rises20 m in 2 s, so the speed is 20 / 2 = 10 m/s. From 2 s to 4 s the line is horizontal, so the speed is 0 m/s.A horizontal section means the object is stationary. A line back to zero means it returned to the start.
A distance-time graph with a horizontal section where the object is at rest and straight sloping sections showing constant speed, the steeper line belonging to the faster object.

Speed-time graphs: gradient is acceleration, area is distance

A speed-time graph plots speed on the vertical axis and time on the horizontal axis. Two things can be read from it, and you must keep them apart. The gradient gives the acceleration and the area under the line gives the distance travelled.

The area rule works because distance = speed x time, and the area of the graph is a speed multiplied by a time. Split the area into rectangles and triangles and work out each one. For a graph that rises from 0 to 20 m/s in 5 s and then holds at 20 m/s, the triangle under the rise is 0.5 x 5 x 20 = 50 m, and a rectangle would be added for any constant-speed section.

Read the shapes the same way as for distance-time graphs, but with a different meaning: a horizontal line is constant speed with zero acceleration, a straight sloping line is constant acceleration, and a curve is changing acceleration. The steeper the line, the greater the acceleration.

Distance-time graph: gradient = speed. Speed-time graph: gradient = acceleration and area = distance. Learn both pairs before the exam.
A velocity-time graphThe gradient is the acceleration. The area between the line and the time axis is the distance travelled.0246805101520Time (s)Velocity(m/s)area = distance travelled3 s x 12 m/s = 36 mconstant velocity 12 m/sacceleration is zeroacceleratinggradient = accelerationdeceleratinggradient = -4.0 m/s2Rising lineVelocity increases, so theacceleration is positive.Horizontal lineVelocity is constant, so theacceleration is zero.Falling lineVelocity decreases, so theobject is decelerating.Area under the lineDistance travelled. Split itinto a rectangle and a triangle.Reading the graphAcceleration = gradient = change in velocity / change in time. From 0 s to 2 s the velocityrises 12 m/s in 2 s, so a = 12 / 2 = 6.0 m/s2. From 2 s to 5 s the line is horizontal, so a = 0.Distance = area under the line. The shaded rectangle is 3 s x 12 m/s = 36 m.
A speed-time graph with a straight sloping section (constant acceleration), a horizontal section (constant speed) and a falling section (deceleration); the gradient of each section gives the acceleration and the area under the line gives the distance travelled.

Acceleration and deceleration: a = change in velocity / time

Acceleration is the change in velocity per unit time. The equation is a = (v - u) / t, where u is the initial velocity, v is the final velocity, t is the time taken and a is the acceleration in m/s2 (metres per second squared).

The unit m/s2 means the velocity changes by that many metres per second every second. An acceleration of 3 m/s2 means the object gains 3 m/s of speed each second. Starting from rest and accelerating at 3 m/s2 for 4 s gives a final speed of 3 x 4 = 12 m/s.

Put it into the equation: a car speeds up from 8 m/s to 20 m/s in 4.0 s. a = (v - u) / t = (20 - 8) / 4.0 = 12 / 4.0 = 3.0 m/s2.

Deceleration is simply a negative acceleration: the velocity is decreasing. If the final velocity is smaller than the initial velocity the value of a comes out negative. A train slowing from 25 m/s to rest in 5.0 s has a = (0 - 25) / 5.0 = -5.0 m/s2, which is a deceleration of 5.0 m/s2. Give either the negative acceleration or the positive deceleration, but do not write a negative number and call it a deceleration of -5.0 m/s2 - that is a double negative, and it says the train is speeding up.

QuantityEquationUnit
Speedv = s / tm/s
Average speedtotal distance travelled / total time takenm/s
Accelerationa = (v - u) / tm/s2
Acceleration of free fall gapproximately constant near the Earth's surface9.8 m/s2
Every answer needs a unit: m/s for a speed or velocity and m/s2 for an acceleration.

Free fall and terminal velocity

Near the surface of the Earth the acceleration of free fall, g, is approximately constant at 9.8 m/s2. Every object dropped near the Earth's surface accelerates downwards at this rate, whatever its mass, provided that air resistance is negligible. After 3 s of free fall from rest an object is moving at 9.8 x 3 = 29.4 m/s.

In air, though, a falling object feels two forces: its weight pulling it down and air resistance (drag) pushing it up. At the start the weight is much larger than the drag, so there is a large resultant force downwards and the object accelerates at close to g.

As the object speeds up, the drag grows, so the resultant force becomes smaller and the acceleration falls. Eventually the drag grows until it is equal to the weight. The two forces cancel, the resultant force is zero, the acceleration is zero, and the velocity stops increasing. This constant velocity is the terminal velocity.

A skydiver reaches terminal velocity after a few seconds of falling. When the parachute opens the drag suddenly becomes much larger than the weight, so the resultant force is upwards, the skydiver decelerates, and then a new and much lower terminal velocity is reached. In a vacuum there is no drag at all, so a feather and a hammer fall together with the same acceleration g.

At terminal velocity the forces have not disappeared - the weight is still there. The drag has simply grown until it balances the weight, so the resultant force is zero and the acceleration is zero.

Key terms you must be able to define

Speed
The distance travelled per unit time, given by v = s / t and measured in m/s.
Velocity
Speed in a given direction; a vector, measured in m/s, so '20 m/s due east' is a velocity and '20 m/s' is a speed.
Average speed
The total distance travelled divided by the total time taken; the single steady speed that would cover the same journey in the same time.
Acceleration
The change in velocity per unit time, given by a = (v - u) / t and measured in m/s2.
Deceleration
A negative acceleration, in which the velocity decreases; a deceleration of 5.0 m/s2 is the same as an acceleration of -5.0 m/s2.
Gradient
The slope of a graph, found by dividing the change in the vertical value by the change in the horizontal value; the gradient is the speed on a distance-time graph and the acceleration on a speed-time graph.
Acceleration of free fall (g)
The acceleration of an object falling under gravity alone, approximately constant near the Earth's surface at 9.8 m/s2.
Terminal velocity
The constant velocity reached by a falling object when the upward air resistance equals the downward weight, so the resultant force and the acceleration are both zero.

Applied to the real world

Cambridge sets physics in unfamiliar contexts - a car braking, a power station, a hospital scanner, a satellite. Use these as models for how to apply the physics, then write your own.

On the road

A speed camera times a car over a measured stretch of road and divides the distance by the time to get the average speed. A car that covers the 500 m between the marks in 25 s has an average speed of 500 / 25 = 20 m/s, which is 72 km/h. The camera uses average speed because it is the steady speed that would cover the section in the same time, and that is what the law limits.

In a car

When a driver brakes, the car decelerates. A car travelling at 30 m/s that stops in 5.0 s has an acceleration of (0 - 30) / 5.0 = -6.0 m/s2, a deceleration of 6.0 m/s2. The stopping distance is the area under its speed-time graph, 0.5 x 5.0 x 30 = 75 m. Doubling the speed roughly quadruples the braking distance, which is why speed limits matter so much.

In sport

A sprinter accelerates out of the blocks. Reaching 10 m/s in 2.0 s means an acceleration of (10 - 0) / 2.0 = 5.0 m/s2. Coaches use speed-time graphs from video analysis to see exactly when an athlete is still accelerating and when top speed is reached, because a runner only improves if the acceleration phase is measured rather than guessed.

In free fall

A skydiver jumps from a plane and at first accelerates at about 9.8 m/s2. As the speed builds, air resistance grows until it balances the skydiver's weight, and the velocity becomes constant at the terminal velocity, about 50 m/s for a person spread out. Opening the parachute increases the drag, so the skydiver slows to a new and much lower terminal velocity and lands safely.

Flashcards

Click a card to flip it. Mark honestly — the tracker uses this.

Q1Define speed.
The distance travelled per unit time, given by v = s / t and measured in m/s.
Q2What is the difference between speed and velocity?
Velocity is speed in a given direction; speed has size only, while velocity has size and direction.
Q3What is the equation for average speed?
Average speed = total distance travelled / total time taken.
Q4What does the gradient of a distance-time graph give?
The speed of the object.
Q5What does the gradient of a speed-time graph give?
The acceleration of the object.
Q6What does the area under a speed-time graph give?
The distance travelled.
Q7Define acceleration.
The change in velocity per unit time, given by a = (v - u) / t and measured in m/s2.
Q8What is the unit of acceleration?
m/s2, metres per second squared; it means the velocity changes by that many m/s every second.
Q9State the acceleration of free fall near the Earth's surface.
g is approximately constant at 9.8 m/s2.
Q10What is a deceleration?
A negative acceleration, in which the velocity decreases; a deceleration of 4 m/s2 is an acceleration of -4 m/s2.
Q11On a distance-time graph, what does a horizontal line show?
The object is at rest, because its distance is not changing.
Q12On a speed-time graph, what does a horizontal line show?
Constant speed, so the acceleration is zero.
Q13What is terminal velocity?
The constant velocity a falling object reaches when the upward drag equals its downward weight, so the resultant force and the acceleration are both zero.
Q14Why do a feather and a hammer fall with the same acceleration in a vacuum?
There is no air resistance, so the only force is weight and gravity gives every object the same acceleration g, whatever its mass.
0 of 14 marked as known

Exam-style questions

9 questions, 24 marks. Write your answer, then reveal the mark scheme and tick each point you actually made. Answering honestly here is what makes the rest of the site useful.

StateAO11 mark
State what is meant by the velocity of an object.

Mark scheme — tick each point you actually made

Examiner tip: The direction is the mark. A statement of speed alone is not a definition of velocity.
CalculateAO22 marks
A cyclist travels a distance of 1500 m in a time of 120 s. Calculate the average speed of the cyclist.

Mark scheme — tick each point you actually made

Examiner tip: Show the equation and the substitution, then give the answer with its unit. A bare 12.5 scores at most one mark.
DetermineAO23 marks
On a distance-time graph a straight line passes from 0 m at 0 s to 40 m at 8 s. Determine the speed of the object during this section.

Mark scheme — tick each point you actually made

Examiner tip: Divide distance by time, not time by distance. If your unit comes out as s/m the gradient has been turned upside down.
DescribeAO13 marks
A speed-time graph has three sections: a straight line from 0 m/s at 0 s to 15 m/s at 5 s, then a horizontal line at 15 m/s from 5 s to 15 s, then a straight line falling from 15 m/s at 15 s to 0 m/s at 20 s. Describe the motion of the object in each of the three sections.

Mark scheme — tick each point you actually made

Examiner tip: Say whether the change is constant. 'It goes faster' is not enough; the shape of the line shows constant acceleration.
DetermineAO23 marks
For the speed-time graph in the previous question, determine the total distance travelled by the object.

Mark scheme — tick each point you actually made

Examiner tip: Split the shape into triangles and rectangles and show each area. Using the height of the line as the distance is a common and costly error.
CalculateAO23 marks
A car accelerates from 8.0 m/s to 20 m/s in a time of 4.0 s. Calculate the acceleration of the car.

Mark scheme — tick each point you actually made

Examiner tip: Take the initial velocity from the final velocity. Remember the unit is m/s2, not m/s.
DeduceAO22 marks
A train travelling at 25 m/s brakes and comes to rest in 5.0 s. Deduce the acceleration of the train and state its deceleration.

Mark scheme — tick each point you actually made

Examiner tip: The negative sign is the mark. Give either -5.0 m/s2 or a deceleration of 5.0 m/s2, but never both signs together.
ExplainAO25 marks
A skydiver jumps from an aircraft and eventually reaches terminal velocity. Explain, in terms of the forces acting on the skydiver, why the acceleration decreases as they fall and why the velocity then becomes constant.

Mark scheme — tick each point you actually made

Examiner tip: Link the growing drag to the shrinking resultant force, then to the falling acceleration. Say drag equals weight, not that the forces disappear.
ExplainAO22 marks
State the acceleration of free fall near the Earth's surface and explain why, in a vacuum, a heavy object and a light object fall with the same acceleration.

Mark scheme — tick each point you actually made

Examiner tip: Give the value to two significant figures or better, and link the equal acceleration to the absence of air resistance.

Exam technique for this topic

  • Always give the unit with a speed or an acceleration: m/s for speed and velocity, m/s2 for acceleration. A bare number loses a mark.
  • Keep the two graphs apart. On a distance-time graph the gradient is the speed; on a speed-time graph the gradient is the acceleration and the area is the distance.
  • For the area under a speed-time graph, split the shape into triangles and rectangles and show each area separately. Use 0.5 x base x height for a triangle.
  • A deceleration is a negative acceleration. Write the value with its sign, or state the magnitude and call it a deceleration, but never give a negative number labelled as a deceleration.
  • Check the units before you substitute: a time in minutes must be multiplied by 60, and a distance in km must be multiplied by 1000.
  • For terminal velocity, the key idea is that the resultant force is zero because drag equals weight, so the acceleration is zero. Do not say there is no force or no gravity.

Why students lose marks here

A student wroteA student wrote: 'The gradient of a speed-time graph gives the distance travelled.'
Why it loses marksThis mixes up the two graphs. The gradient of a speed-time graph gives the acceleration; the distance comes from the area under the line. Confusing gradient with area is the commonest error in graph questions.
The answer that scoresOn a speed-time graph the gradient is the acceleration, because acceleration is the change in velocity divided by the time. The distance travelled is the area under the line, because distance is speed multiplied by time. On a distance-time graph it is the other way round: the gradient there is the speed.
A speed camera records how long a car takes to cross a measured distance, an everyday use of speed = distance / time.
A student wroteA student wrote: 'At terminal velocity the skydiver stops accelerating because there are no forces acting on them.'
Why it loses marksForces do not vanish. The weight and the air resistance are both still acting; they have become equal and opposite, so the resultant force is zero. Saying there are no forces is a physics error and loses the mark.
The answer that scoresAt terminal velocity the downward weight is balanced by the upward air resistance (drag). The resultant force is zero, so the acceleration is zero and the velocity stays constant. The forces are still there - they simply cancel out.
A student wroteA student wrote: 'A train slows from 20 m/s to rest in 4 s, so its deceleration is -5 m/s2.'
Why it loses marksThis is a double negative. A deceleration is already a negative acceleration, so calling -5 m/s2 a deceleration of -5 m/s2 says the train is speeding up. Examiners want either a negative acceleration or a positive deceleration, not both.
The answer that scoresa = (v - u) / t = (0 - 20) / 4 = -5 m/s2. This can be written as an acceleration of -5 m/s2, or as a deceleration of 5 m/s2. Both are correct; combining the two signs is not.
A student wroteA student wrote: 'The car travelled 15 m because the speed-time graph is 15 m/s high.'
Why it loses marksThe height of a speed-time graph is the speed, not the distance. Reading the y-value as the distance ignores the time altogether and gives an answer with the wrong unit.
The answer that scoresThe distance is the area under the speed-time graph, not the height of the line. A car at a constant 15 m/s for 10 s travels the area of the rectangle, 15 x 10 = 150 m. If the speed is changing, split the area into triangles and rectangles before adding.

Where this fits in IGCSE Physics

This page is one topic of Cambridge IGCSE Physics 0625. IGCSE Physics is the course home: every area and every topic in Cambridge's own order, the papers you sit and what each one tests, and the exam-practice tools. The full topic list, with each topic linked to its revision page, is on the IGCSE Physics syllabus page.