Question

A particle stats with a velocity of $2m{s}^{-1}$ and moved in a straight line with a retardation of $0.1m{s}^{-2}$. The first time at which the particle is $15m$ from the starting point is:

• A. $10s$
• B. $20s$
• C. $30s$
• D. $40s$

Answer 1

The correct option is A $10s$

Time to make the velocity $zero$ and changing the direction of motion, will be given as $T=\frac{u}{a}=\frac{2}{0.1}=20sec$

time needed to cover $15m$ will be given by $s=ut-a{t}^2/2$

so $15=2t-0.05t^2$, multiplying by $20$ both sides we get $t^2-40t+300=0$

solving it we get $t=30sec$ and $t=10sec$

$t=10sec$ is the first moment when the particle will be at $15m$