Question

A car of 1500kg is moving at a velocity of 60km/hr. Find the work done to stop this car.

Answer 1

Hint: A car moving at a constant velocity possesses kinetic energy. To stop the car the same amount of energy must be supplied.

Complete step by step solution:
Step 1: Listing the information provided in the question.
From the question we have, the mass of the car is $m = 1500{\text{kg}}$ .
Also, it moves at velocity of $v = 60{\text{km/hr}}$ .
Step 2: Finding the kinetic energy of the car.
The car of $m = 1500{\text{kg}}$ moves at a velocity of $v = 60{\text{km/hr}}$.
Expressing velocity in S. I. units, $v = 60 \times \dfrac{5}{{18}} = 16.66{\text{m/s}}$
The relation for kinetic energy of a moving body is given by, $k = \dfrac{1}{2}m{v^2}$.
Substituting for mass $m$ and velocity $v$ in the above relation, the kinetic energy of the car is obtained as, $k = \dfrac{1}{2}\left[ {1500 \times {{\left( {16.66} \right)}^2}} \right] = 208.166{\text{kJ}}$ .
Step 3: Defining work and finding the work done to stop the car.
Work can be defined as the energy transferred when a force applied on an object causes a displacement. Here the car already in motion possesses kinetic energy. Now, to stop the moving car some work needs to be done. When the car comes to rest, its kinetic energy becomes zero.
The change in kinetic energy is given by $208.166{\text{ kJ}} - 0{\text{ kJ}}$ .
As work is a transfer of energy, ${\text{work done = change in kinetic energy}}$.

Therefore, the required amount of work to be done to stop the car will be $208.166{\text{kJ}}$.

Additional information:
Work is also defined as the dot product of the force applied to the body and the displacement caused. Force and displacement are vector quantities (i.e., have both direction and magnitude). Since work is the dot product of two vectors, it is a scalar quantity (i.e., work has no direction, only magnitude).

Note:
Before substituting values in an equation, always make sure that the quantities are expressed in their S. I. units. As work is a transfer of energy it has the same S. I. unit as that of energy, i.e., kJ.