Question

the kinetic energy of an object of mass m moving with a velocity of 25m/s. If it comes to rest by covering a distance of 12 meter after the application of brakes. Find the work done it and value of braking force.


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Answer 1

Given :

• Initial velocity of the object (u) = 25 m /s
• Final velocity (v) = 0 m/s
• Distance covered by the object (s) = 12 m
• Mass of the object = m

To find:

• Breaking force
• Acceleration

How to solve:

• First, we need to find the acceleration of the object. As the object is moving uniformly we can apply the third equation of motion to find acceleration.
• The second step is to find the force acting on the object this can be found using Newton's second law.
• The last step is to find the word done. We know that the work done by an object is a scalar product of force and displacement. Simply substitute the values to get the final answer.

Solution:

By applying the third equation of motion,

$\blacksquare \:$v ²= u² + 2as

Now let's substitute the values,

⇒ 0 = 625 + 2 x a x 12

⇒ a = 625 / 24

⇒ a = 26.04 m/s²

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Now,

By Newton's second law,

$\blacksquare \:$F = ma

⇒ F = 26.04 m N

( As the value of mass is not given to us)

The force acting on the body is 26.04m  N.

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Work done by the object is given by,

$\blacksquare \:$W = F.s

⇒ W = 26.02 m  x  12

⇒ W = 312.48m J

The work done by the object is 312.48m J.