A car accelerates uniformly from velocity u to velocity v in time t. On the graph, which area equals the distance travelled by the car in time t ?

Question 17

A car accelerates uniformly from velocity u to velocity v in time t.

On the graph, which area equals the distance travelled by the car in time t ?

A NPTU + PQST

B NPW V + VRSU

C NPW V + WRST

D PST + PQS

Reference: Past Exam Paper – June 2016 Paper 11 Q6

Solution:

Answer: B.

Distance travelled is obtained from the area under the velocity-time graph.

Distance travelled in time t = area of trapezium PSTUN

Area of trapezium = Area of triangle PST + Area of rectangle PTUN

Choice A: gives an overestimate of the required area as the area of the triangle PQS should not be included.

Choice B: gives the correct area

If the graph is divided into 2 parts: (i) from time = 0 to time = t/2 and (ii) time = t/2 to time = t

Area NPWV gives an underestimation as the area of the triangle above NPWV is missing.

Area VRSU gives an overestimation as the triangle above the line should not be included.

However, when both are considered, the underestimation and overestimation cancel out giving the correct area.