Speed, velocity and acceleration GCSE physics lesson: a = Δv/t and v² − u² = 2as

Speed, velocity and acceleration: practice

Show your working on paper. Velocities are in m/s, times in seconds, distances in metres. Write a deceleration with a minus sign. The scenes are virtual experiments: work out what you expect first, then move only the setting the question names. The stretch is optional.

Diagnostic question: choose and explain

1. A car speeds up steadily from 4 m/s to 12 m/s over a distance of 32 m. What is its acceleration?
   1. 0.25 m/s²
   2. 1 m/s²
   3. 2 m/s²
   4. 4 m/s²

Practice questions

1. A bus speeds up from 2 m/s to 8 m/s in 4 seconds. What is its acceleration, in m/s²?
2. Which is closest to a typical speed for a person walking?
   1. 0.15 m/s
   2. 1.5 m/s
   3. 15 m/s
   4. 150 m/s
3. A runner does one 400 m lap of a track in 80 seconds and finishes where she started. Which is right?
   1. Average speed 5 m/s; average velocity 5 m/s
   2. Average speed 5 m/s; average velocity 0 m/s
   3. Average speed 0 m/s; average velocity 0 m/s
   4. Average speed 0.2 m/s; average velocity 0 m/s
4. Sort each quantity: a scalar (a size only) or a vector (a size and a direction).They sort 8 items into Scalar and Vector.
5. Virtual experiment. A car starts at 4 m/s and speeds up for 6 seconds. Set its acceleration a so that it reaches 13 m/s at the end. Work out what a should be first, then set it.They change an interactive scene (velocity–time) until it does it.
6. Virtual experiment. A cyclist starts from rest and speeds up at 0.5 m/s². How long does she take to travel 25 m? Work it out first: her speed after 25 m with v² − u² = 2as, then the time with a = Δv ÷ t. Then set the time t and check the distance under the line.They change an interactive scene (velocity–time) until it does it.
7. Virtual experiment. A car going at 12 m/s brakes steadily for 3 seconds. Set its acceleration a so that it has just stopped at the end of the 3 seconds. Work out what a should be first, then set it.They change an interactive scene (velocity–time) until it does it.
8. The braking car in the last scene went from 12 m/s to rest at −4 m/s². Use v² − u² = 2as to work out its braking distance, in metres. Does it agree with the distance under the line in the scene?
9. From rest, a car accelerates at 2 m/s² over 25 m. Use v² − u² = 2as to find its final speed, in m/s.
10. A train slows down steadily from 30 m/s to 10 m/s over 400 m. Find its acceleration, in m/s².
11. A skydiver falls at a steady 55 m/s, her terminal velocity. Which is true?
    1. No forces act on her now
    2. Her weight is bigger than the air resistance
    3. Her weight and the air resistance are equal and opposite
    4. Gravity has stopped pulling on her
12. Stretch: a car is going at 108 km/h. That is ___ m/s. It brakes at −6 m/s². Its braking distance is ___ m.

Support: For the scenes: work out what you expect first with the equations, then change only the setting the question lets you move and watch the velocity–time line and its readings. Does it do what you predicted?

Speed, velocity and acceleration: exit

Write u, v, a, s and t first. Show your working on paper.

1. A car brakes steadily from 20 m/s to rest in 4 seconds. What is its acceleration, in m/s²?
2. Use v² − u² = 2as to find how far the same car travels while it brakes, in metres.

Exit check

One acceleration and one braking distance show who can choose and use each equation.

Students write u, v, a, s, t first, then work out a with a = Δv ÷ t.

Speed, velocity and acceleration

For each calculation write u, v, a, s and t first, then the equation, then the numbers. Give units. Take g = 9.8 m/s² and ignore air resistance unless the question says.