Question

A motor cyclist travelling at 12m/s decelerates at 3m/s² a) How long does it take to come to rest?b) How far does he travel in coming to rest?

Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

Initial velocity = 12m/s

Acceleration = -3m/s²

[፨ -ve sign shows retardation]

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

We have to find,

⟶ Time taken by cyclist to come to rest position.

⟶ Distance covered by cyclist before it is brought to rest.

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

⛥ Since, acceleration of motorcyclist is said to be constant throughout the period of motion. So, we can easily solve this question by using equation of kinematics.

⛥ Distance covered by moving object before it is brought to rest is called 'stopping distance.'

✪ Calculation of time :

$:\implies\tt\:v=u+at$

$:\implies\tt\:0=12+(-3)t$

$:\implies\boxed{\bf{\red{t=4\:s}}}$

✪ Calculation of distance :

$:\implies\tt\:v^2-u^2=2as$

$:\implies\tt\:0^2-12^2=2(-3)s$

$:\implies\tt\:s=\dfrac{-144}{-6}$

$:\implies\boxed{\bf{\blue{s=24\:m}}}$