Interpreting gradient and area in context.
10 original questions, 43 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
A car starts from rest and accelerates uniformly to a velocity of 24 m/s in 8 seconds.
It then travels at a constant velocity of 24 m/s for a further 20 seconds.
Water flows into an empty tank. The rate of flow increases uniformly from 0 litres per minute to 12 litres per minute during the first 5 minutes. It then stays at 12 litres per minute for a further 10 minutes.
Work out the total volume of water in the tank after 15 minutes.
The tank holds 200 litres. The flow stays at 12 litres per minute. Work out how many more minutes it takes for the tank to fill. Give your answer in minutes and seconds.
The running cost of a machine is measured in pounds per hour. For the first 2 hours the cost is constant at £6 per hour. Over the next 4 hours the cost increases uniformly from £6 per hour to £14 per hour.
Work out the total cost of running the machine for the 6 hours.
Work out the mean cost per hour over the 6 hours. Give your answer to the nearest penny.
A train travels at a constant velocity of 30 m/s for 40 seconds.
It then decelerates uniformly, coming to rest in a further 25 seconds.
A motorbike accelerates from rest. Its speed-time graph is a smooth curve that gets less steep throughout the first 12 seconds. The table gives the speed v m/s at time t seconds.
t: 0, 4, 8, 12 v: 0, 7, 11, 13
A train travels between two stations. It accelerates uniformly from rest to 18 m/s in 6 seconds, travels at a constant 18 m/s for 14 seconds, then decelerates uniformly to rest in 10 seconds.
Work out the total distance between the two stations.
Work out the average speed for the whole journey.
Write the average speed as a percentage of the maximum speed. Give your answer correct to 1 decimal place.
A lorry starts from rest and accelerates uniformly for 10 seconds until it reaches a velocity of 20 m/s.
It then travels at a constant velocity of 20 m/s for T seconds.
The lorry travels a total distance of 700 m.
Work out the total time of the journey.
The table shows the distance, s metres, travelled by a cyclist from a start line, t seconds after she starts to accelerate.
| t | 0 | 2 | 4 | 6 | 8 | 10 |
|---|---|---|---|---|---|---|
| s | 0 | 6 | 20 | 42 | 72 | 110 |
Work out the average speed of the cyclist over the first 10 seconds.
Estimate the cyclist's speed at t = 6 by working out the gradient of the chord joining the points at t = 4 and t = 8.
What does the gradient of the distance-time graph represent?
A car makes a journey in three stages.
Stage 1: it accelerates uniformly from rest to a velocity of V m/s in 12 seconds.
Stage 2: it travels at the constant velocity V m/s for 48 seconds.
Stage 3: it decelerates uniformly from V m/s to rest in 20 seconds.
The total distance of the journey is 960 m.
The table shows the speed, v m/s, of a motorbike t seconds after it starts to accelerate. The graph of v against t is a smooth curve that gets less steep.
| t | 0 | 5 | 10 | 15 | 20 |
|---|---|---|---|---|---|
| v | 0 | 8 | 13 | 16 | 17 |
Use four trapezia to estimate the distance travelled in the first 20 seconds.
Is your answer an underestimate or an overestimate? Give a reason.
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.