11.6 Gradients and areas under graphs — Practise

Work independently in order. The later questions mix this section with earlier methods. Questions marked H are Higher only.

1. H A velocity rises from 2 m/s to 10 m/s in 4 seconds. Find the gradient.
2. H A velocity-time graph shows 6 m/s for 5 seconds. Find distance travelled.
3. H Velocity rises uniformly from 0 to 8 m/s in 4 seconds. Find distance travelled.
4. H Velocity changes uniformly from 4 to 10 m/s over 3 seconds. Find distance.
5. H A velocity-time line goes from (0,3) to (5,13). Find the acceleration.
6. H What does the area under a velocity-time graph represent?
7. H A runner moves at 4 m/s for 3 seconds, then 2 m/s for 5 seconds. Find total distance.
8. H Water flows at 2 litres per minute for 7 minutes. Find volume transferred using rate times time.
9. H Find the gradient between $(1,3)$ and $(4,12)$, then say if it is greater than the gradient from $(0,0)$ to $(2,5)$.
10. H A velocity-time graph rises from 0 to 12 m/s in 6 s, then stays at 12 m/s for 4 s. Find total distance.