Question

brakes are applied to a car travelling at 72km /h so as to stop it in 4 seconds. Find acceleration and distance covered
If anyone know the answer.. please help me to do this..​

Answer 1

Given :

• Initial velocity of car ,u = 72km/hr=20m/s
• Brakes are applied so that car stops ,final Velocity = 0m/s
• Time ,t = 4sec

To Find :

• Acceleration of the car
• Distance covered by the car

${\purple{\boxed{\large{\bold{Formula's}}}}}$

Kinematic equations for uniformly accelerated motion .

$\bf\:v=u+at$

$\bf\:s=ut+\frac{1}{2}at{}^{2}$

$\bf\:v{}^{2}=u{}^{2}+2as$

and $\bf\:s_{nth}=u+\frac{a}{2}(2n-1)$

Solution :

1) We have to find the acceleration of the car

By equation of motion .

$\sf\:v=u+at$

$\sf\:0=20+a\times4$

$\sf\:-20=4a$

$\sf\:a=\dfrac{-20}{4}$

$\sf\:a=-5ms{}^{-2}$

Here ,negative sign of the acceleration means that it is retardation.

Thus ,the acceleration of the car is -5 m/s².

2) We have to find the distance travelled by the car.

By equation of motion

$\sf\:v^2=u^2+2aS$

$\sf\:0=400+2\times(-5)\times\:S$

$\sf\:10S=400$

$\sf\:S=\dfrac{400}{10}$

$\sf\:S=40m$

Thus,the car covered 40m .

Answer 2

$\bigstar\bf\blue{GIVEN}\bigstar$

• $\bf\red{Initial\:velocity=20m/s^{1}}$

• $\rm\blue{Final\:Velocity=0m/s(As\:the\:brakes\:are\:applied)}$

• $\rm\pink{Time\:Taken=4s.}$

$\bigstar\bf\blue{To\:find}\bigstar$

• The acceleration and Distance Covered by car after the brakes applied.

$\bigstar\bf\blue{FORMULAE:USED}\bigstar$

• ${\boxed{\rm{\blue{a=\dfrac{v-u}{t}}}}}$

Where,

a=Acceleration

v= Final Velocity

u= Initial Velocity

t=Time

• ${\boxed{\rm{\blue{V^2-u^2=2as}}}}$

Where,

a=Acceleration

v= Final Velocity

u= Initial Velocity

S= Distance.

Now,

$\implies\rm{a=\dfrac{v-u}{t}}$

$\implies\rm{a=\dfrac{0-20}{4}}$

$\implies\rm{a=\dfrac{\cancel{-20}}{\cancel{4}}}$

$\implies\rm{a=-5m/s^{2}}$

Now, Using third equation of motion

$\implies\sf{v^2-u^2=2as}$

$\implies\sf{(0)^2-(20)^2=2\times{(-5)}(s)}$

$\implies\sf{0-400=-10s}$

$\implies\sf{S=\dfrac{\cancel{-400}}{\cancel{-10}}}$

$\implies\sf{ S= 40m}$