Question

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

Answer 1

using second equation of motion
v^2-u^2=2as
where v=0 due to coming in rest and a =-a because it deaccelerates from high velocity to low
so
u^2=2as
a=9m/s^2
now force = mass × acc.
force = 1000 × 9 = 9000N exerted by brake
work = force × displaced distance in direction of force
work = 9000× 50 = 450000 joule

Answer 2

Question

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

Answer

Mass of the car [m] = 1000kg

Initial velocity of the car [u] = 30 m/s

Final velocity of the car [v] = 0 m/s

Distance covered [S] = 50m

Force applied by brakes [F] = ?

Work done by Brakes [W] = ?

Firstly, we try to find the Force applied by brakes. But we dont have the acceleration produced. So we use Laws of Motion.

v² - u² = 2as

0² - 30² = 2a[50]

- 900 = 100a

$\mathsf{\frac{- 900}{+ 100}}$ = a

a =  - 9 m/s²

---------------------------

Now, we find out the Force applied by the brakes.

Force = Mass × Acceleration

F = ma

F = 1000 × -9

$\large\boxed{\huge{\mathsf{F = -9000N}}}}$

-------------------------

Now, we find the Work done by the Brakes.

Work Done = Force × Distance

W = F × S

W = -9000 × 50

W = -450000J

       OR

$\large\boxed{\huge{\mathsf{W = -450KJ}}}}$