Question

Let $v_A$ and $v_B$ be the velocities of the particles A and B respectively at the moment A and B meet after start of the motion. If $u_A=5m{s}^{-1}$ and $u_B=15m{s}^{-1},$ then the magnitude of the difference of velocities $v_A$ and $v_B$ is

• A. $5m{s}^{-1}$
• B. $10m{s}^{-1}$
• C. $15m{s}^{-1}$
• D. data insufficient

Answer 1

Answer: (B)

$10m{s}^{-1}$

As given, let $\alpha$ be the acceleration of object A and $\beta$ be the deceleration of object B.

Let these 2 objects meet (have same displacement ) in time $t_1$

So, by equating the equations for their displacements, we get

$5t_1+0.5\alpha t_1^2$ = $15t_1-0.5\beta t_1^2$

Or $(\alpha +\beta )t_1=20$

Now, as given,

$v_{A}and{v}_B$ are the velocities of objects A and B when they meet.

so, $v_A=u_A+\alpha t_1$ $v_A=5+\alpha t_1$

and $v_B=u_B-\beta t_1$ $v_B=15-\beta t_1$

Subtracting above two equations, we get

$v_A-v_B$ = $-10$ + $(\beta +\alpha )t_1$ = $-10+20$ = $10$m/sec Option B