Motion: Speed, Velocity and Acceleration
Speed, velocity and acceleration describe and calculate motion, distinguishing scalar quantities such as speed from vector quantities such as velocity, and using equations linking speed, velocity, acceleration, distance and time. It also covers terminal velocity, the constant speed a falling object reaches once its weight and drag forces balance.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Identify what is being asked (speed, distance, time or acceleration) and choose the matching equation: speed = distance / time; acceleration = (final velocity - initial velocity) / time taken; or, at higher tier, (final velocity)^2 = (initial velocity)^2 + 2 x acceleration x distance, for problems with no time given.
- Convert units so they match before substituting into an equation, for example changing minutes to seconds, or km/h to m/s, and check the final unit matches what the question asks for.
- On a distance-time graph, read the gradient as speed (a steeper line means a faster speed, a flat horizontal line means the object is stationary, and a curve means the speed is changing).
- On a velocity-time graph, read the gradient as acceleration and the area between the line and the time axis as the distance travelled; split the area into simple shapes (triangles and rectangles) when the graph has multiple sections.
- For a terminal velocity question, explain the motion in stages: describe the initial resultant force and acceleration, explain how the resistive force changes as speed increases, and finish by explaining why the object stops accelerating once the forces balance.
- Show full working with units at each step of a calculation, and state the final answer with the correct unit, to a sensible number of significant figures.
Worked example
A cyclist accelerates uniformly from a velocity of 2 m/s to a velocity of 11 m/s in 6 seconds. Calculate the cyclist's acceleration.
- Write down the equation: acceleration = (final velocity - initial velocity) / time taken.
- Identify the values: final velocity = 11 m/s, initial velocity = 2 m/s, time taken = 6 s.
- Substitute the values: acceleration = (11 - 2) / 6.
- Calculate: acceleration = 9 / 6 = 1.5.
- Final answer: the cyclist's acceleration is 1.5 m/s^2.
Practice questions
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Q1Define the term 'vector quantity' and give one example.Show answer
Answer: A quantity with both magnitude and direction, for example velocity, displacement, acceleration or force.
Q2A runner completes a 400 m race in 52 s. Calculate her average speed, giving your answer to 3 significant figures.Show answer
Answer: 7.69 m/s (400 / 52 = 7.6923..., rounded to 7.69).
Q3State what the gradient of a distance-time graph represents.Show answer
Answer: Speed.
Q4A car's velocity increases from 8 m/s to 20 m/s over 4 seconds. Calculate its acceleration.Show answer
Answer: 3 m/s^2 ((20 - 8) / 4 = 3).
Q5A skydiver reaches terminal velocity during free fall. Explain what is meant by 'terminal velocity'.Show answer
Answer: The constant, maximum velocity reached by a falling object once the resultant force on it is zero, because air resistance has increased to become equal in size to weight, so the object stops accelerating.
Q6A train travels at a constant velocity of 40 m/s for 3 minutes. Calculate the distance it travels, in km.Show answer
Answer: 7.2 km (distance = speed x time = 40 x 180 = 7200 m = 7.2 km).
Q7On a velocity-time graph, what does the area between the line and the time axis represent?Show answer
Answer: The distance travelled (or displacement).
Q8A ball decelerates uniformly from 18 m/s to 0 m/s over a distance of 2.7 m while being caught. Using (final velocity)^2 = (initial velocity)^2 + 2 x acceleration x distance, calculate its deceleration.Show answer
Answer: 60 m/s^2 (0 = 18^2 + 2 x a x 2.7, so a = -324 / 5.4 = -60, giving a deceleration of 60 m/s^2).
Exam-style questions
Written in the style of a GCSE Science exam paper, with a full mark scheme.
A delivery van's velocity over 30 seconds is as follows: from 0 to 10 s the van accelerates uniformly from 0 m/s to 12 m/s; from 10 s to 22 s the van travels at a constant 12 m/s; from 22 s to 30 s the van decelerates uniformly from 12 m/s back to 0 m/s. (a) Calculate the van's acceleration during the first 10 seconds. (b) Calculate the total distance travelled by the van during the whole 30 seconds.
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A stone is dropped from rest from a bridge and falls for 1.8 s before hitting the water below. Using the equation v = u + at, and taking the acceleration due to gravity as 9.8 m/s^2, calculate the velocity of the stone as it hits the water.
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Explain, using ideas about forces, how a skydiver's velocity changes from the moment they jump from a plane to the moment they reach a constant velocity, before opening their parachute.
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See real GCSE Science past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the motion: speed, velocity and acceleration worksheet pack - 14 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 13 of GCSE Physics Workbook, the whole course as one free printable PDF.
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