Question

a robber riding on a bike on a straight road. see a police van standing 190m a head and applies breakes.this causes the bike to slow down at rate of 15m/s-²if he takes 5s to stop the bike.explain whether it will or will not. hit the van
​

Answer 1

Answer:

Bike will not hit the police van.

Explanation:

Given that:

As brakes are applied, so Retardation = 15 $ms^{-2}$

$\Rightarrow a=-15\ ms^{-2}$

Time taken, $t = 5s$

Finally, the bike will stop, so final speed, $v =0\ m/s$

Let $u$ be the initial speed.

Formulae:

$1.\ v =u+at\\2.\ s=ut+\dfrac{1}{2} a t^{2}$

Using formula (1), we can find the initial speed of bike and then by putting values of $u, v, a$ and $t$, we can find the distance traveled by the bike before stopping.

Using Formula 1:

$0 = u + (-15) \times (5)\\\Rightarrow u = 75\ m/s$

Putting values  $u, v, a$ and $t$ in Formula (2):

$s = 75 \times 5 + \dfrac{1}{2} \times (-15) \times 5^{2} \\\Rightarrow s = 375 - \dfrac{1}{3} \times 375\\\Rightarrow s = \dfrac{375}{2}\\\Rightarrow s = 187.5\ m$

It is given that distance between police van and robber is 190m.

But, actually as per the given statement, 187.5m distance will be traveled by bike before stopping which is lesser than 190m.

Hence, the bike will not hit the police van.