Question

A body travelling with uniform acceleration crosses two points $A$ and $B$ with velocities $20m/sec$ and $30m/sec$ respectively then the speed of the body at mid point of $A$ and $B$ is

• A. $25.5m/sec$
• B. $24m/sec$
• C. $10\sqrt{6}m/sec$
• D. $25m/sec$

Answer 1

Answer: (A)

Let the acceleration of the car is $=a$ and the distance between $A$ and $B$ is $=d$

$v^2-u^2=2ad$

Given,

$v=30m/s$ and $u=20m/s$

$2ad={30}^2-{20}^2$

$ad=\frac{(900-400)}{2}=250$

when the car is at the mid point of $AB$ then let the speed of the car is

$v_1$

$v_1^2-{20}^2=2a\left(\frac{d}{2}\right)$

$v_1^2=ad+400=250+400=650$

therefore

$v_1$ is $=25.5m/s$