Question

Two cars A and B of equal masses $100kg$ are moving on a straight horizontal road with same velocity $3m/s$. At t$=$ 0 car A starts accelerating with constant acceleration of $2m/s^2$ (initial separation between cars is $25m$. Choose correct options (neglect length of cars)

• A. car A catches car B at t $=$ 6 sec.
• B. total work done of all forces on car B w.r.t. car A is zero in first 2 sec.
• C. car A catch car B at t$=$ 5 sec.
• D. total work done by all forces on car A w.r.t. car B is nonzero in first 2 sec.

Answer 1

Answer: (C), (D)

The correct options are
C car A catch car B at t$=$ 5 sec.
D total work done by all forces on car A w.r.t. car B is nonzero in first 2 sec.

Consider relative motion of A w.r.t. B
$a=2m/s^2$ $u=0$ $s=25m$ {A w.r.t. B}
$s=ut+\frac{1}{2}a{t}^2$
$\Rightarrow 25=0+\frac{1}{2}2t^2$
$\Rightarrow t=5seconds.$
and $\Delta K.E.$ of one car w.r.t. other car is not zero in first 2 sec.