Question

A filled shopping cart (30.0 kg) is being pushed rapidly towards the back of a store so that its velocity is 2.0 m/s. What is the momentum of the cart and what is the kinetic energy of the cart?
A. 90 kg m/s and 60 J
B. 60 kg m/s and 90 J
C. 60 kg m/s and 60 J
D. 90 kg m/s and 90 J

Answer 1

The momentum of the body is equal to the product of its mass and its velocity. Recall the formula for the kinetic energy of the body in terms of its mass and velocity. The S.I unit of kinetic energy is joule.

Formula used:
Momentum, $p = mv$
Here, m is the mass and v is the velocity.
Kinetic energy, $K = \dfrac{1}{2}m{v^2}$

Complete step by step answer:
We have given the mass of the cart $m = 30.0\,{\text{kg}}$ and its velocity is $v = 2.0\,{\text{m/s}}$. We know that the momentum of the body is equal to the product of its mass and its velocity. Therefore, the linear momentum of the cart is,
$p = mv$
Here, m is the mass and v is the velocity.
Substituting $m = 30.0\,{\text{kg}}$ and $v = 2.0\,{\text{m/s}}$ in the above equation, we get,
$p = \left( {30.0} \right)\left( {2.0} \right)$
$\Rightarrow p = 60.0\,{\text{kg}}\,{\text{m/s}}$
Therefore, the momentum of the cart is 60 kg m/s.
We have the expression for the kinetic energy of the body.
$K = \dfrac{1}{2}m{v^2}$
Substituting $m = 30.0\,{\text{kg}}$ and $v = 2.0\,{\text{m/s}}$ in the above equation, we get,
$K = \dfrac{1}{2}\left( {30} \right){\left( 2 \right)^2}$
$\therefore K = 60\,{\text{J}}$
Therefore, the kinetic energy of the cart is 60 J.

So, the correct answer is option C.

Note: Instead of using the formula, $K = \dfrac{1}{2}m{v^2}$, students can use the relation between the kinetic energy and linear momentum, $K = \dfrac{{{p^2}}}{{2m}}$. Note that the derived unit of kinetic energy is joule but there is no such unit for the momentum of the particle. To use the formula for momentum, $p = mv$, the velocity v must be uniform.