Question

Study the given paragraph(s) and answer the following questions.

A thief is running on a motorcycle at a constant speed of$25m{s}^{-1}$. A police jeep starts chasing from a point $1.25\mathrm{km}$ behind him with a uniform acceleration of $2{\mathrm{ms}}^{-2}$.

After how much time will the police catch the thief?

• A. $1minutes$
• B. $1.5minutes$
• C. $2minutes$
• D. $50seconds$

Answer 1

The correct option is D

$50seconds$

Step 1: Given

The initial velocity of the thief is $u_t=25{\mathrm{ms}}^{-1}$

The initial velocity of the police jeep w.r.t thief's motorcycle,
$$\begin{gathered} u_{pt}=u_p-u_t=-25{\mathrm{ms}}^{-1} \\ {u}_p=0initially \end{gathered}$$
Acceleration of police jeep w.r.t thief's motorcycle,
$a_{pt}=a_p-a_t=2{\mathrm{ms}}^{-2}$

Step 2: Solution

Using, $s=ut+\frac{1}{2}a{t}^2$,

Here $s$ is displacement and $u$ is initial velocity and $a$ is acceleration and$t$ is time.

we get$1250=-25t+t^2$
or$t^2-25t-1250=0$
or $t=50\mathrm{s},-25\mathrm{s}$
but time cannot be-ve,

$\therefore t=50\mathrm{s}$

Hence the correct option is D.