Velocity–time graphs GCSE lesson: acceleration as gradient, distance as area

Velocity–time graphs: practice

Show your working on paper. Velocities are in m/s, times in seconds. Write a negative acceleration with a minus sign. The stretch is optional.

Diagnostic question: choose and explain

1. A velocity–time graph is a flat line at 5 m/s from 0 to 10 seconds. What does it show?
   1. Standing still
   2. Moving at a steady 5 m/s
   3. Speeding up by 5 m/s every second
   4. It has gone 5 m in the 10 seconds

Practice questions

1. A car's velocity rises steadily from 0 to 20 m/s in 4 seconds. What is its acceleration in m/s²?
2. A runner keeps a steady 8 m/s for 15 seconds. How many metres does she run?
3. From rest, a car speeds up steadily to 10 m/s in 4 seconds. How many metres does it go in those 4 seconds?
4. On a velocity–time graph a straight line goes from (0, 12) to (6, 0). What is the acceleration in m/s²?
5. A velocity–time line slopes down from 12 m/s to 0. What is the object doing?
   1. Coming back to where it started
   2. Slowing down, still moving forwards
   3. Going downhill
6. Two cars' velocity–time lines cross at (4, 10). What does that tell you?
   1. They are in the same place at 4 seconds
   2. They have gone the same distance after 4 seconds
   3. Both are going at 10 m/s at 4 seconds
7. A train speeds up from 0 to 20 m/s in 10 seconds, stays at 20 m/s for 30 seconds, then slows to 0 in 20 seconds. How many metres does it travel?
8. A car going at 4 m/s speeds up steadily for 10 seconds and covers 90 m. What is its velocity at the end, in m/s?
9. As the lights turn green, a cyclist rides past at a steady 6 m/s and a car pulls away from rest, speeding up by 2 m/s every second. After how many seconds does the car catch the cyclist?
10. Stretch: a curved velocity–time graph goes through (0, 0), (2, 3) and (4, 8), and bends upwards. Two trapezia estimate the distance in the first 4 seconds as ___ m. Is that an overestimate or an underestimate? ___

Support: For question 3: draw it. The area is a triangle, base 4 s and height 10 m/s: ½ × base × height. For question 4: the gradient is the change in velocity ÷ the time, and the velocity goes down.

Velocity–time graphs: exit

Show your working; one sentence for the last part.

1. A cyclist speeds up steadily from 2 m/s to 8 m/s in 6 seconds. Find the acceleration and the distance travelled. Say which part of the velocity–time graph gives each.

Exit check

One acceleration and one distance, each named as gradient or area, show who has both ideas.

A cyclist speeds up steadily from 2 m/s to 8 m/s in 6 seconds. Sketch the velocity–time graph.

Velocity–time graphs: gradients and areas

Sketch a velocity–time graph for each question before working anything out. Say whether each answer comes from a gradient or an area, and give its units.