Question

If you are given with a force of magnitude $25N$ acting on a body of mass $2kg$ increases its kinetic energy from $100J$ to $200J$. The displacement of the body during this interval.

Answer 1

Here we have to use the concept that work done by the force should be equal to change in its kinetic energy. We know the initial and final kinetic energy of the body from which we can calculate the change in kinetic energy. Now using the work done formula we can find the displacement of the body during that interval.

Complete step by step answer:
As per problem we have a force of magnitude $25N$ acting on a body of mass. $2kg$ increases its kinetic energy from $100J$ to $200J$.
We know that the work done by a body due to application of some external force is equal to the change in kinetic energy of the body.
Mathematically we can write,
$\Delta KE = W$
According to the problem the change in kinetic energy is from $100J$ to $200J$.
Where the final kinetic energy is equal to $200J$ and the initial kinetic energy is equal to $100J$.
Hence,
$\Delta KE = K{E_f} - K{E_i}$
$\Rightarrow \Delta KE = 200J - 100J = 100J \ldots \ldots \left( 1 \right)$
We know the work done is the product of force, F and displacement, d of the body.
Mathematically we can write,
$W = Fd$
$\Rightarrow W = 25N \times d \ldots \ldots \left( 2 \right)$
Equation equation $\left( 1 \right)$ and $\left( 2 \right)$ we will get,
$100J = 25N \times d$
$\Rightarrow \dfrac{{100J}}{{25N}} = d$
Hence the displacement of the body is $4m$.

Note: Kinetic energy is a form of energy that an object or a particle has by reason of its motion. Also remember that if work that transfers energy is done on a body by applying a net force then the body speeds up and due to which it gains the kinetic energy.