Question

a car initially moving with a uniform velocity of 72 km/hour and comes to stop after 10 seconds .Calculate the retardation of the car and also find the acceleration

Answer 1

Given:

Initial velocity of car, u= 72 km/h

Final velocity of car, v=0 km/h

Time taken by car, t= 10 s

To Find:

Retardation and acceleration of car

Solution:

We know that,

According to first equation of motion for constant acceleration,

$\purple{\boxed{\bf{v=u+at}}}$

where,

v is final velocity

u is initial velocity

a is acceleration

$\rule{190}{1}$

It is given that,

$\longrightarrow\rm{u=72\:km/h=72\times\dfrac{5}{18}\:m/s=20\:m/s}$

$\longrightarrow\rm{v=0\:km/h=0\times\dfrac{5}{18}\:m/s=0\:m/s}$

Let the acceleration of car be 'a'

On using first equation of motion on car, we get

$\longrightarrow\rm{v=u+at}$

$\longrightarrow\rm{0=20+a(10)}$

$\longrightarrow\rm{-20=10a}$

$\longrightarrow\rm{10a=-20}$

$\longrightarrow\rm{a=\dfrac{-20}{10}}$

$\longrightarrow\rm\green{a=-2\:m/s^{2}}$

If acceleration is -2 m/s², then retardation will be 2 m/s² because value retardation is just opposite to acceleration in sign.

Hence, acceleration of car is -2 m/s² and retardation is 2 m/s².