Question

a car a mass of 2000kg traveling at 15 m/s stop at a distance of 100 m decelerating uniformly. what is the force exerted on it brakes? what is the work done by the brakes ?

Answer 1

This is the answer for the given question. .

Answer 2

Given :-

Mass of the car = 1000 kg

Initial velocity of the car = 30 m/s

Final velocity = 0 m/s ( The car stops )

Distance = 50 m

To be calculated :-

What is the force exerted on it by the brakes?

What is the work done by the brakes?

Solution :-

In order to calculate the force , we have to find out acceleration first .

Now,

we know that :-

v² = u² + 2as

where ,

v = final velocity

u = initial velocity

a = acceleration

s = distance

putting the values in the above formula we get ,

v² = u² + 2as

⟹ ( 0 )² = ( 30 )² + 2 × a × 50

⟹ 100a = - 900

⟹ a = -900 / 100

⟹ a = -9

⟹ a = -9 m/s²

Note : negative denotes retardation

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Now let's find the force exerted by the brakes can be calculated by using the formula :-

⟹ F = m × a

⟹ F = 1000 x -9

⟹ F = - 9000 N

⟹ |F| = 9000 N

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Now ,

we find the work done by the brakes by using the relation :

⟹ W = F × s

here,

force ( F ) = 9000 N

Distance ( s ) = 50 m

So ,

Work done ( W ) = 9000 × 50 J

⟹ W = 450000 J

⟹ $W$ = 4.5 × 10⁵ J

Hence ,

the work done by the brakes is 4.5 × 10⁵ joules

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