Speed, velocity and accelerationIB MYP Physics: Revision notes
Section 1
Speed and velocity
Speed tells you how fast something moves. It is a scalar, with no direction.
speed = distance ÷ time (v = s ÷ t), measured in m/s.
Velocity is speed in a given direction, so it is a vector. A car going round a roundabout at a steady 10 m/s has constant speed but changing velocity, because its direction keeps changing.
Average speed = total distance ÷ total time for the whole journey. Instantaneous speed is the speed at one moment, like the reading on a car's speedometer. During a journey the instantaneous speed changes, but the average speed is a single value.
Velocity and speed are not the same. An object moving in a circle at constant speed has a changing velocity.
Section 2
Calculating speed
Rearrange v = s ÷ t as needed:
- distance s = v × t
- time t = s ÷ v
Worked example: a cyclist rides 90 m in 15 s. Speed = 90 ÷ 15 = 6 m/s. At 6 m/s she would take 300 ÷ 6 = 50 s to ride 300 m.
Watch the units: change km to m (×1000) and minutes to seconds (×60) before you divide.
A track lap is 400 m. If it takes 50 s, the average speed is 400 ÷ 50 = 8 m/s.
Section 3
Acceleration
Acceleration is the rate of change of velocity.
a = (v − u) ÷ t
where u is the starting (initial) speed, v the final speed and t the time taken, in seconds. The unit is m/s² (metres per second per second).
- Speeding up gives a positive acceleration.
- Slowing down gives a negative acceleration, called deceleration.
- Uniform acceleration means the velocity changes by the same amount every second.
Worked example: a car speeds up from 5 m/s to 25 m/s in 10 s. a = (25 − 5) ÷ 10 = 2 m/s².
Rearranged: v = u + at.
Acceleration is not speed. A fast car at a steady 30 m/s has zero acceleration.
Section 4
Measuring speed
Light gates: a card of known length is fixed to a moving trolley. When it passes through the light gate it blocks the beam, and a timer records the time. Speed = length of card ÷ time for the card to pass. This gives a speed close to the instantaneous speed at the gate. Two gates give two speeds, and the time between them gives the acceleration.
Ticker timer: a paper tape is pulled through a timer that makes a dot at regular time intervals (for example every 0.02 s). Widely spaced dots mean fast movement; dots getting further apart mean acceleration. The distance between dots divided by the time between them gives speed.
Section 5
Free fall
An object falling with only gravity acting on it is in free fall. Near the Earth's surface its acceleration is g = 10 m/s², the same for all objects when air resistance is ignored.
So a dropped ball gains 10 m/s of speed every second: 10 m/s after 1 s, 20 m/s after 2 s, 30 m/s after 3 s (v = gt starting from rest).
In real life air resistance reduces the acceleration of light, large objects like feathers or paper much more than that of dense, compact objects.
Must know
- Speed = distance ÷ time (m/s); velocity is speed in a given direction.
- Average speed is for the whole journey; instantaneous speed is at one moment.
- Acceleration = (v − u) ÷ t, in m/s²; negative means deceleration.
- Light gates and ticker timers measure speed.
- Free-fall acceleration g = 10 m/s².
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Speed, velocity and acceleration
- A runner in Kingston, Jamaica, completes one 400 m lap of an oval running track in 50 s. The track has two straight sections and two curved bends. A stopwatch measures the time for the whole lap.Even if the runner keeps a constant speed of 8 m/s, explain why her velocity changes as she runs round a bend.2 marks
- A train leaves a station in Mumbai. It accelerates uniformly from rest to 20 m/s in 40 s on a straight track. Later, approaching the next station, it brakes uniformly from 20 m/s to rest in 10 s.Calculate the speed of the train 24 s after it leaves the station.2 marks
- A student in Lagos investigates free fall. She drops a card 12.0 cm long through two light gates, one above the other. The first light gate records that the card blocks the beam for 0.060 s. The second light gate records that the card blocks the beam for 0.020 s. The time for the card to fall from the first light gate to the second is 0.40 s. The accepted value for the acceleration of free fall is 10 m/s².Calculate the speed of the card as it passes through the first light gate.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).