Rates Of Change

60.
The diagram shows a speed-time graph for a journey of a car.
0 1 2 3 4 5 6 7 8 0 5 10 15 20 25 30 Speed (m/s) Time (sec)

(a) Calculate:
(i) the retardation at t=27 sec
(ii) the distance travelled for the whole journey
(b) On the grid, draw the distance-time graph of the car's journey.
0 25 50 75 100 125 150 200 0 5 10 15 20 25 30 Distance (m) Time (sec)
(a)(i) ......................... [1] (a)(ii) ......................... [1] (b) See graph [3]
Paper 1
61.
A car travels 50 km at a speed of 40 km/h. The journey starts at 12:10. Work out the time the journey finishes.
................................. [2]
Paper 1
1.
A bus travelling at an average speed of 45 km/h left the bus stop at 8.15 am.
A taxi left the bus stop at 9.00 am and overtook the bus at 10.45 am.

(i) How much time, in hours, did the taxi take before overtaking the bus.
......................... hours [2]
(ii) Find the average speed of the taxi.
......................... km/h [3]
Paper 3
2.
Pule rode a bicycle from home to school at a constant speed. The distance from home to school is 7.2 km.
At 0700, he had travelled one-sixth of the total distance. At 0708, he had travelled half of the total distance.

(a) Find the fraction of the total distance Pule had travelled from 0700 to 0708.
......................... [2]
(b) Calculate:
(i) the distance Pule had travelled from 0700 to 0708,
......................... km [2]
(ii) the speed, in kilometres per hour, at which Pule was cycling from 0700 to 0708.
......................... km/h [3]
(c) If Pule left home at 0656, find the time at which he arrived at school.
......................... [2]
(d) One Saturday, Pule cycled from home to the shop at an average speed of 16 km/h for 30 minutes. He then cycled from the shop to Malingoaneng at an average speed of 16 km/h for 15 minutes. Calculate the total distance travelled from home to Malingoaneng.
......................... km [4]
Paper 3
3.
The graph shows a bus travelling from Maseru to Leribe and back to Maseru.
0 20 40 60 80 0900 1000 1100 1200 1300 1400 1500 1600 1700 Distance (km) Time

(a) Find the distance from Maseru to Leribe.
......................... km [1]
(b) How long does the bus stay at Leribe? Give your answer in hours and minutes.
......................... h min [2]
(c) What happened at 1500?
......................... [1]
(d) (i) Between which times is the bus travelling faster?
......................... [1]
(ii) At what speed is the bus travelling on this part of the journey?
......................... km/h [2]
(e) Calculate the average speed for the journey from Leribe to Maseru.
......................... km/h [2]
Paper 3
4.
An insect covers 12 mm per step.

(i) Calculate the number of steps needed to cover 2.4 m.
......................... [2]
(ii) If it takes 5 × 10−2 seconds for each step, how long does it take to travel 3 m?
......................... s [2]
Paper 3
5.
The distance from Botha-Bothe to Maseru is 123 km.

(a) Thato drove the 123 km in 2 hours 19 minutes. Calculate her average speed. State the units of your answer.
......................... km/h [3]
(b) The amount of petrol Thato's car used for the journey was 23 litres, correct to the nearest litre.
(i) Write down the least possible amount of petrol used.
......................... litres [1]
(ii) Write down the greatest possible amount of petrol used.
......................... litres [1]
Paper 3
6.
Mosa drove from her home to the airport. She waited at the airport. Then she drove home. Here is the distance-time graph for Mosa's complete journey.
0 10 20 30 40 50 1400 1430 1500 1530 1600 1630 Distance from home (km) Time of day

(a) What is the distance from Judy's home to the airport?
......................... km [1]
(b) For how many minutes did Judy wait at the airport?
......................... min [1]
(c) Work out Judy's average speed on her journey home from the airport. Give your answer in kilometres per hour.
......................... km/h [2]
Paper 3