Question

A car weighing 1000 kg and travelling at 30 m/s stops at a distance of 50 m decelerating uniformly. What is the force exerted on it by the brakes? What is the work done by the brakes?

9th Class Please​

Answer 1

$\bf \large{Given : }$

• Initial Speed(u) = 30 m/sec

• Distance (s) = 50 m

• Mass = 1000 kg

$\bf \large{To \: Find : }$

• Force Exerted on the car by the brakes.

• Work Done by the brakes.

$\bf \large{Solution : }$

We've to Find Acceleration first to calculate the Force.

We know that :

$\star \: \boxed{ \sf {v}^{2} = {u}^{2} + 2as}$

$\longrightarrow \sf \: ({0})^{2} = {(30})^{2} + 2 \times a \times 50$

$\longrightarrow \sf \: 0 = 900 + 100a$

$\longrightarrow \sf \: 100a = - 900$

$\longrightarrow \sf \: a = \cancel\dfrac{ - 900}{100}$

$\longrightarrow \sf \: a = - 9m / {sec}^{2}$

Let's Find Force Now :

$\star \: \boxed{ \sf \: Force = Mass \times Acceleration}$

$\longrightarrow \sf \:Force = 1000 \times ( - 9)$

$\longrightarrow \sf \:Force = - 9000 \: Newton$

Thus,Force exerted on the car by the brakes is -9000 Newtons.

[As it is Negative The Force Exerted is Retarding Force]

Now, We've to find the Work Done by the brakes.

We know that :

$\star \: \boxed{ \sf \: Work = Force \times Distance }$

$\longrightarrow \sf \: Work = -9000 \times 50$

$\longrightarrow \sf \: Work = -450000 \: Joules$

$\longrightarrow \sf \: Work = -4.5 \times {10}^{5} \: Joules$

Thus,The Work Done by the brakes is -4.5× 10^5 Joules.

Answer 2

Force  = - 9000 newton

Work done by car = - 45000 joules

 Explanation:

Given :

Initial velocity (u) = 30 m/s

Final velocity (v) = 0 m/s

weight of car = 1000 kg

 distance traveled by of car after applying brakes =50 m

To find :

1)  force exerted on it by the brakes

2) work done by the brakes

 Solution:

$v^{2} = u ^{2} +2as$

$(0 m/s)^{2} = (30 m/s)^{2} + 2 (a)(50 m)$

$(0 m/s)^2$ = (900) + 2 a× 100 m

a = -900/100

a = -9$m/s^2$

As we know that the acceleration  is decelerating it means that the acceleration is negative .

⇒a =  - 9 $m/s^2$

the force of car = mass× acceleration

                          =  m× a

                          =  1000 × (-9)

                           = - 9000 newton

work done by the brakes = force × distance

                                           = ( -9000 newton)× (50 m)

                                           = -450000 joule

Force=  The force of a body is equal to the product of its mass and acceleration.

Work done = work done in a moving body is equal to the product of force  exerted on the body and distance covered by it.