Question

Two masses $A$ and $B$ are moving in the same straight line, A moves with a uniform velocity of $11m/sec$, $B$ starts from rest at the instant when it is $52.5$ metres ahead of $A$, and moves with a uniform acceleration $1m/{sec}^2$. When will $A$ catch $B$? Explain the reason for two answers?

Answer 1

Let the time after which they meet be $t$.

Since B is $52.5m$ ahead of A, then equation of motion for B is,

$11t=\frac{1}{2}\times 1\times t^2+52.5$

$22t=t^2+105$

$t^2-22t+105=0$

$\left(t-7\right)\left(t-15\right)=0$

$t=7s$ Or $t=15s$

If they move in opposite direction, they will meet in 7 seconds and if they move in the same direction, they will meet in 15 seconds.