Question

The velocity – time graph of a car moving on a straight road is shown: Calculate the acceleration of the car during the last 8 seconds:


(A) $ - 2.5m/{s^{ - 2}}$
(B) $ - 1.5m/{s^{ - 2}}$
(C) $0$
(D) Cannot be determined from the given plot

Answer 1

Hint: To answer this question we need to consider the acceleration of the car at every part of the graph. The graph is to be divided in sections as per the diagram and on the basis of the coordinates covered by the graph, we have to determine the acceleration. The time coordinate will help us to find the acceleration of the car specifically for the last 8 seconds.

Complete step by step answer:
 We should know the formula of finding the acceleration.
The acceleration of the car will be given as the distance covered divided by the time taken.
From the graph we can determine that the acceleration of the car in the last 8 seconds will be given by the slope of the line BC.
To find the slope of BC we can write it as: $\dfrac{{BD}}{{CD}}$
From the graph we can put the values as:
$\dfrac{{(0 - 20)}}{{(13 - 5)}} = \dfrac{{ - 20}}{8} = - 2.5m{s^{ - 2}}$
So we can say that the acceleration of the car in the last 8 seconds is $ - 2.5m/{s^{ - 2}}$.

Hence Option A is correct.

Note: To avoid any difficulty while solving such type of questions we should be knowing that, we need to consider the part of the graph covered by the line of the object in the distance coordinate and time coordinate. The acceleration can be negative as well as positive depending on the slope of the line which depicts the movement of the object.