Question

A thief on a bike moving with uniform velocity passes a stationary policeman who is hiding behind a bill board with a motorcycle. After a 2.0 sec. delay (reaction time) the policeman accelerates to his maximum speed of 150 km/hr in 12sec. The policeman moves with uniform speed of 150 km/hr from this instant onwards and catches up with the thief 1.5 km beyond the billboard. Find the speed of the thief in km/hr.

Answer 1

Given,

$t=2s$

$Speed=150km/h$ in $12s$

So,

Let the policeman caught the thief after time t,

So, distance traveled by them is 1500m

Let v is the speed of the thief,

$v=\frac{ds}{dt}=\frac{1500}{t}$

Initial speed of the the policeman is zero,

And, the final speed after $12s$ is $150km/h=\frac{125}{3}m/s$

So,

$v=u+at$

$\frac{125}{3}=0+12a$

$a=\frac{125}{36}$

Now,

Distance traveled in $12s$

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

$0+\frac{1}{2}\times \frac{125}{36}\times {12}^2$

$=250m$

Now, Distance traveled in time $t=$Distance traveled in $12s+$ Distance traveled in $t-12-2$

Because of $2s$ is the response time.

Thus,

$1500=250+\frac{125}{3}\times (t-12-2)$

$t=44s$

Thus, the velocity of the thief is:

$\frac{1500}{44}=34.09m/s$

Hence, the speed of the thief in $km/hr$ is:

$7km/h$