CAMBRIDGE IGCSE MATHS (0580)
Paper 2 (P2): SPEED, DISTANCE & TIME -1 Topic Quiz
Distances from the Sun can be measured in astronomical units (AU). Earth is 1 AU from the Sun, and one AU is approximately 1.496 × 10⁸ kilometers. Complete the following table by calculating the missing distances:
| Name | Distance from the Sun in AU | Distance from the Sun in kilometers |
|---|---|---|
| Earth | 1.0 | 1.496 × 10⁸ |
| Mercury | 0.387 | ? |
| Jupiter | ? | 7.79 × 10⁸ |
| Pluto | ? | 5.91 × 10⁹ |
Light travels at approximately 300,000 kilometers per second. Earth is 1 AU from the Sun, and 1 AU is approximately 1.496 × 10⁸ kilometers. How long does it take light to travel from the Sun to Earth? Give your answer in seconds.
Light travels at approximately 300,000 kilometers per second. Pluto is approximately 5.91 × 10⁹ kilometers from the Sun. How long does it take light to travel from the Sun to Pluto? Give your answer in minutes.
One light year is the distance light travels in one year (365 days). Light travels at approximately 300,000 kilometers per second. Calculate how far one light year is in kilometers and give your answer in standard form.
One AU is approximately 1.496 × 10⁸ kilometers. Use your answer from Question 4 to calculate how many astronomical units (AU) are equal to one light year.
Emily cycles along a path for 2 minutes. She starts from rest and accelerates at a constant rate until she reaches a speed of 5 m/s after 40 seconds. She continues cycling at 5 m/s for 60 seconds, then decelerates at a constant rate until she stops after a further 20 seconds. Draw a speed-time graph to represent Emily's journey.
During the first 40 seconds of Emily's journey, she accelerates at a constant rate from rest to a speed of 5 m/s. Calculate Emily's acceleration.
Emily's total journey lasts 2 minutes. Calculate her average speed for the entire journey.
The diagram shows the speed-time graph for a car travelling between two sets of traffic lights.
(i) Calculate the deceleration of the car for the last 5 seconds of the journey.
(ii) Calculate the average speed of the car between the two sets of traffic lights.
Chuck cycles along Skyline Drive. He cycles 60 km at an average speed of x km/h. He then cycles a further 45 km at an average speed of (x + 4) km/h. His total journey time is 6 hours.
(i) Write down an equation in x and show that it simplifies to 2x² - 27x - 80 = 0.
(ii) Solve 2x² - 27x - 80 = 0 to find the value of x.
The diagram shows the speed-time graph for a car travelling along a road for T seconds. To begin with, the car accelerated at 0.75 m/s² for 20 seconds to reach a speed of v m/s.
(i) Show that the speed, v, of the car is 15 m/s.
(ii) The total distance travelled is 1.8 kilometres. Calculate the total time, T, of the journey.
Asma runs 22 kilometres, correct to the nearest kilometre. She takes 2 1/2 hours, correct to the nearest half hour.
Calculate the upper bound of Asma’s speed.
Ricardo asks some motorists how many litres of fuel they use in one day. The numbers of litres, correct to the nearest litre, are shown in the table.
| Number of litres | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|
| Number of motorists | 11 | 10 | p | 4 | 8 |
(i) For this table, the mean number of litres is 17.7. Calculate the value of p.
(ii) Find the median number of litres.
Manuel completed a journey of 320 km in his car. The fuel for the journey cost $1.28 for every 6.4 km travelled.
(i) Calculate the cost of fuel for this journey.
(ii) When Manuel travelled 480 km in his car it used 60 litres of fuel. Manuel’s car used fuel at the same rate for the journey of 320 km. Calculate the number of litres of fuel the car used for the journey of 320 km.
(iii) Calculate the cost per litre of fuel used for the journey of 320 km.
Ellie drives a car at a constant speed of 30 m/s, correct to the nearest 5 m/s. She maintains this speed for 5 minutes, correct to the nearest 10 seconds.
Calculate the upper bound of the distance in kilometres that Ellie could have travelled.
The cost of 1 apple is a cents. The cost of 1 pear is p cents.
The total cost of 7 apples and 9 pears is 354 cents.
(i) Write down an equation in terms of a and p.
(ii) The cost of 1 pear is 2 cents more than the cost of 1 apple. Find the value of a and the value of p.
Rowena walks 2 km at an average speed of x km/h.
(i) Write down an expression, in terms of x, for the time taken.
(ii) Rowena then walks 3 km at an average speed of (x - 1) km/h. The total time taken to walk the 5 km is 2 hours.
(a) Show that 2x² - 7x + 20 = 0.
(b) Find the value of x. Show all your working and give your answer correct to 2 decimal places.
The graph shows information about the journey of a train between two stations.
(i) Work out the acceleration of the train during the first 4 minutes of this journey. Give your answer in km/h².
(ii) Calculate the total distance, in kilometres, between the two stations based on the journey shown in the graph.
The train is moving at a speed of 126 km/h.
(i) Show that 126 km/h is equivalent to 35 m/s.
The train has a total length of 220 m. At 09:30, the train begins crossing a bridge that has a length of 1400 m.
(ii) Calculate the time, in seconds, the train takes to completely cross the bridge.
On a different journey, the train took 73 minutes, correct to the nearest minute, to travel 215 km, correct to the nearest 5 km.
Calculate the upper bound of the average speed of the train for this journey. Give your answer in km/h.
Luigi and Alfredo run in a 10 km race. Luigi’s average speed was x km/h, while Alfredo’s average speed was 0.5 km/h slower than Luigi’s average speed.
(a) Luigi took 10/x hours to run the race. Write down an expression, in terms of x, for the time that Alfredo took to run the race.
(b) Alfredo took 0.25 hours longer than Luigi to run the race.
- (i) Show that 2x² - x - 40 = 0.
- (ii) Use the quadratic formula to solve 2x² - x - 40 = 0. Show all your working and give your answers correct to 2 decimal places.
- (iii) Work out the time that Luigi took to run the 10 km race. Give your answer in hours and minutes, correct to the nearest minute.
The diagram shows the speed−time graph for part of a journey for two people, a runner and a walker.
(a) Calculate the acceleration of the runner for the first 3 seconds.
........................................ m/s²
(b) Calculate the total distance travelled by the runner in the 19 seconds.
............................................ m
(c) The runner and the walker are travelling in the same direction along the same path. When t = 0, the runner is 10 metres behind the walker. Find how far the runner is ahead of the walker when t = 19.
A cyclist completes a 60-second journey as described below:
(a) The cyclist accelerates uniformly from rest to 12 m/s in the first 8 seconds. Calculate the acceleration of the cyclist.
........................................ m/s² [1]
(b) The cyclist maintains a constant speed of 12 m/s for the next 32 seconds. Calculate the distance traveled by the cyclist during this time.
............................................ m [2]
(c) The cyclist decelerates uniformly to rest over the remaining 20 seconds. Calculate the total distance traveled by the cyclist during the entire journey.
............................................ m [3]
A train completes a 90-second journey as described below:
(a) The train accelerates uniformly from rest at a rate of 1.5 m/s² for the first 20 seconds. Calculate the speed of the train at the end of 20 seconds.
........................................ m/s [1]
(b) The train travels at a constant speed for the next 50 seconds. Calculate the distance traveled by the train during this period.
............................................ m [2]
(c) The train decelerates uniformly to rest over the final 20 seconds. Find the total time taken for the journey and the total distance traveled.
............................................ m [3]
A runner completes a 25-second sprint as described below:
(a) The runner accelerates uniformly from rest to 8 m/s in 4 seconds. Calculate the acceleration of the runner.
........................................ m/s² [1]
(b) The runner maintains a constant speed of 8 m/s for the next 16 seconds. Calculate the distance traveled by the runner during this period.
............................................ m [2]
(c) The runner decelerates uniformly to rest over the final 5 seconds. Find the total distance traveled by the runner during the sprint.
............................................ m [3]
