Question

A body moving in straight line with uniform acceleration crosses at two points $A$ and $B$ with velocities $30m/s$ and $60m/s$ respectively. The speed of the body when it crosses one third of the distance between $A$ and $B$ after crossing from $A$ is :

• A. $30\sqrt{2}m/s$
• B. $20/2m/s$
• C. $40/2m/s$
• D. $25/2m/s$

Answer 1

The correct option is A $30\sqrt{2}m/s$

Given,

$u=30m/s$ velocity at point $A$

$v=60m/s$ velocity at point $B$

3rd equation of motion,

$2aS=v^2-u^2$

$2aS=(60{)}^2-(30{)}^2$

$aS=1350$. . . .(1)

When the car is at one third of $AB$,

$2a\frac{S}{3}=v_1^2-(30{)}^2$

$\frac{2}{3}aS=v_1^2-900$

$\frac{2}{3}\times 1350=v_1^2-900$ (from 1)

$900=v_1^2-900$

$v_1^2=1800$

$v_1=30\sqrt{2}m/s$