Speed, velocity and accelerationIB MYP Sciences: Revision notes
Section 1
Speed and distance
Speed tells you how fast something is moving. It is the distance travelled divided by the time taken.
speed = distance ÷ time (v = s ÷ t)
Speed is measured in metres per second (m/s); you may also see km/h. To rearrange the equation:
- distance = speed × time
- time = distance ÷ speed
Worked example: a runner covers 400 m in 50 s. Speed = 400 ÷ 50 = 8 m/s.
The speed of a whole journey is the average speed = total distance ÷ total time. Real objects speed up and slow down, so the speed at any one moment can be different from the average.
Convert the time into seconds before you divide, for example 2 minutes = 120 s.
Section 2
Scalars and vectors
A scalar quantity has size only. A vector quantity has size and direction.
- Scalars: distance, speed, time, mass
- Vectors: displacement, velocity, force, acceleration
Distance is how far you travel along your path. Displacement is your straight-line change of position from the start, in a stated direction.
Vectors are shown with a direction, for example 5 m/s north, or with a positive and negative sign (+ for one way, − for the opposite way).
Section 3
Velocity
Velocity is speed in a given direction, so it is a vector. Two cars each travelling at 20 m/s have the same speed, but if one goes north and the other south they have different velocities.
Velocity can change when the speed changes or when the direction changes, even if the speed stays the same. A car going round a bend at a steady 15 m/s is changing its velocity.
Average velocity = change of position (displacement) ÷ time. A bus that returns to its starting point has an average velocity of 0 m/s, even though its average speed is not zero.
Speed and velocity are not the same thing. Mention direction whenever the question says velocity.
Section 4
Acceleration
Acceleration is how quickly velocity changes.
acceleration = change in velocity ÷ time taken
a = (v − u) ÷ t, where u is the starting velocity and v is the final velocity. The unit is metres per second squared (m/s²).
- Speeding up: positive acceleration.
- Slowing down: negative acceleration, also called deceleration.
- Constant velocity: acceleration is zero.
Worked example: a car goes from 10 m/s to 25 m/s in 5.0 s. a = (25 − 10) ÷ 5.0 = 3.0 m/s².
Use the change in velocity (final minus initial), not just the final velocity.
Section 5
Rearranging equations and calculating
You can rearrange both equations. Use a formula triangle or do the same thing to both sides.
- v = s ÷ t, so s = v × t and t = s ÷ v
- a = Δv ÷ t, so Δv = a × t and t = Δv ÷ a
Worked example: how long does a car take to increase its velocity by 20 m/s at an acceleration of 2.5 m/s²? t = Δv ÷ a = 20 ÷ 2.5 = 8.0 s.
Always write the equation, substitute with units, then give the answer with its unit.
Must Know
- speed = distance ÷ time, in m/s
- Scalars have size only; vectors have size and direction
- Velocity is speed in a given direction
- acceleration = change in velocity ÷ time, in m/s²
- Slowing down is negative acceleration (deceleration)
- Average speed = total distance ÷ total time
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Speed, velocity and acceleration
- A cycling club in Nairobi times one of its riders over a straight 1200 m stretch of road. The rider takes 80 s to cover it.The rider keeps the same average speed. Calculate the distance she travels in 2.0 minutes.2 marks
- A sports car on a test track in Dubai starts from rest and accelerates in a straight line, reaching 27 m/s after 6.0 s.A different car increases its velocity by 20 m/s with an acceleration of 2.5 m/s². Calculate the time this takes.2 marks
- Aiko, a student in Osaka, investigates how the height of a ramp affects the speed of a toy car. She releases the car from rest at the top of the ramp and uses a stopwatch to time how long it takes to cross a 1.0 m flat track at the bottom. Each time is the mean of three runs. The mean times are 2.0 s for a ramp height of 5 cm, 1.4 s for 10 cm, 1.1 s for 15 cm and 1.0 s for 20 cm.State a testable hypothesis for this investigation, giving a scientific reason, and identify the dependent variable.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).