Question

Two cars $A$ and $B$ are moving along straight line with constant acceleration as shown in the velocity-time graph.

The correct relation between their accelerations is

• A. $a_{A}>a_{B}$
• B. $a_{A} < a_{B}$
• C. $a_{A}=a_{B}$
• D. $a_{A}=a_{B} / 2$

Answer 1

Answer: (A)

For motion with uniform acceleration, the $v-t$ graph is a straight line inclined to time axis. Slope of the $v-t$ graph gives the value of constant acceleration.
Also, slope of a straight line in general $=\tan \theta$, where $\theta$ is the angle in the anti-clockwise direction, which the line makes with the positive direction of time axis.
So, in the given graph as shown below

$\beta>\alpha \Rightarrow \tan \beta>\tan \alpha$
Hence , $a_{A}>a_{B}$