Real-Life Graphs (Cambridge (CIE) IGCSE Maths: Extended)

The diagram shows the speed–time graph for the final 40 seconds of a car journey.

At the start of the 40 seconds the speed is m/s.

Find the acceleration of the car during the first 24 seconds.  

 ......................................... m/s²

The diagram shows the speed–time graph of a train journey between two stations.

Find the acceleration of the train during the first 40 seconds.  

................................................ m/s²

Calculate the distance between the two stations.  

................................................ m

The speed–time graph shows the first 50 seconds of a journey.

Calculate the acceleration during the first 15 seconds.  

.............................................m/s²

Calculate the distance travelled in the 50 seconds.  

.................................................m

The diagram shows the speed−time graph for part of a journey for two people, a runner and a walker.

Calculate the acceleration of the runner for the first 3 seconds.   

........................................ m/s² 

Calculate the total distance travelled by the runner in the 19 seconds.  

............................................ m

The runner and the walker are travelling in the same direction along the same path.

When  = 0, the runner is 10 metres behind the walker.  

Find how far the runner is ahead of the walker when  = 19.  

............................................ m

The diagram shows the speed–time graph for 60 seconds of a car journey.

Change 90 km/h to m/s.

.......................................... m/s 

Find the deceleration of the car in m/s².

.........................................m/s²

Find the distance travelled, in metres, in the 60 seconds.

.............................................m

The diagram shows the speed–time graph for the final 40 seconds of a car journey.

At the start of the 40 seconds the speed is m/s.

The total distance travelled during the 40 seconds is 1.24 kilometres.

Find the value of .  

................................................ 

The speed–time graph shows information about a train journey.

By drawing a suitable tangent to the graph, estimate the gradient of the curve at .

What does this gradient represent?

Work out the distance travelled by the train when it is travelling at constant speed.

.............................................. km

Jalina left her home at 10 00 to cycle to a park.

On her way to the park, she stopped at a friend’s house and then continued her journey to the park.

Here is the distance-time graph for her journey to the park.

On her journey to the park, did Jalina cycle at a faster speed before or after she stopped at her friend’s house?

Give a reason for your answer.

Jalina stayed at the park for 45 minutes.

She then cycled, without stopping, at a constant speed of 16 km/h from the park back to her home.

Show all this information on the distance-time graph.

Work out Jalina’s average cycling speed, in kilometres per hour, for the complete journey to the park and back.

Do not include the times when she was not cycling in your calculation.

Give your answer correct to 1 decimal place.

.........................km/h