Question

A motorcycle and a bus are moving with the same momentum which of them has greater kinetic energy?

Answer 1

Step 1: Given data.

It is given that, the momentum of motorcycle and bus is equal.

Step 2: Formula to be used.

1. The formula of momentum $p$ of an object having mass $m$ and velocity $v$ is defined as $p=mv$.
2. The formula of the kinetic energy $K.E$ of an object having mass $m$ and velocity $v$ is defined as $K.E=\frac{1}{2}m{v}^2$.

Step 3: Find the relation between the kinetic energy of the motorcar and the bus.

Assume that, $m_c$ be the mass of the motorcycle and $v_c$ be the velocity of the motorcycle.

Also, $m_b$ be the mass of the bus and $v_b$ be the velocity of the bus.

We know that the mass of the bus is always greater than the mass of the motocycle.

That is, $m_c<m_b$.

Since, $m_c{v}_c=m_b{v}_b...1$.

which implies that, $v_c>v_b$.

Divide both sides by $2$.

$\frac{1}{2}{v}_c>\frac{1}{2}{v}_b$

Now, multiply both sides by $m_c{v}_c$.

$\frac{1}{2}{m}_c{v}_c^2>\frac{1}{2}{m}_c{v}_c{v}_b$

From equation $1$.

$\frac{1}{2}{m}_c{v}_c^2>\frac{1}{2}{m}_c{v}_b^2$

This implies that the kinetic energy of the motorcycle is greater than the kinetic energy of the bus.

Therefore, the motorcycle has greater kinetic energy.