Question

A man travelling in a car with a maximum constant speed of $20\text{m/s}$ watches the friend start off at a distance $100\text{m}$ ahead on a motor cycle with constant acceleration ‘$a$’. The maximum value of ‘$a$’ for which the man in the car can reach his friend is

• A. $2{\text{m/s}}^2$
• B. $1{\text{m/s}}^2$
• C. $4{\text{m/s}}^2$
• D. None of these

Answer 1

The correct option is A $2{\text{m/s}}^2$

$v^2-u^2=2a{S}_{rel}$
For the man to reach his friend, his friend should not be faster than him until he moves a relative displacement of $100\text{m}$ w.r.t his friend
Initial velocity of motorcycle $=0$
$\Rightarrow {20}^2>2a\left(100\right)$
$\Rightarrow a<2{\text{m/s}}^2$
Hence, the maximum value of $a$ is $2{\text{m/s}}^2$