Question

A loaded transport truck with a mass of 38000kg is travelling at \[1.20m/s\] . What will be the velocity of a 1400kg car if it has the same momentum?
A) $32.57m/s$
B) $30m/s$
C) $15m/s$
D) $32.67m/s$

Answer 1

Hint: We can find the momentum of truck (\[{P_{truck}} = {\text{ }}{m_{truck}} \times {v_{truck}}\]). According to the question, the momentum of the truck is equal to the momentum of the car which will help us to find the velocity of the car.

Formula used:
$p = m \times v$
Where, $p$ is the momentum, $m$ is the mass and $v$ is the velocity.

Complete Step by Step Answer:
Let a loaded truck with a mass (\[{m_{truck}}\]) be travelling at the velocity (\[{v_{truck}}\]). Let us assume that the momentum of the truck (\[{P_{truck}}\]) is given as-
\[{P_{truck}} = {\text{ }}{m_{truck}} \times {v_{truck}}\]
From the question, we have -
\[{m_{truck}} = 38000{\text{ }}kg\]
\[{v_{truck}} = 1.2{\text{ }}km/s\]
Now, putting the values in the equation of momentum, we get-
\[
\Rightarrow {P_{truck}} = 38000 \times 1.2 \\
\Rightarrow {P_{truck}} = 45600{\text{ }}kgm/s \\
 \]
According to the question, it is given that the momentum of car is equal to momentum of truck i.e.
\[{P_{truck}} = {P_{car}}\]
Let a car with a mass (\[{m_{car}}\]) be travelling at the velocity (\[{v_{car}}\]). Let us assume that the momentum of the car (\[{P_{car}}\]) is given as-
\[{P_{car}} = {m_{car}} \times {v_{car}}\]
or we can write this equation as following,
\[{v_{car}} = \dfrac{{{P_{car}}}}{{{m_{car}}}}\]
From the question, we have
\[{m_{car}} = 1400kg\]
\[\Rightarrow {v_{car}} = \dfrac{{45600}}{{1400}}\]
\[\Rightarrow {v_{car}} = 32.57m/s\]

Therefore, the car of mass \[1400{\text{ }}kg\] and the same momentum as the truck will have the speed \[32.57{\text{ }}m/s\]. So, option (A) is correct.

Note:
We know that if a body has a mass \[m\] and the velocity \[v\] then the momentum of the body is the product of mass of the body and the velocity of the body. The momentum is a vector quantity. momentum is the product of a scalar and a vector. The momentum of the truck and the car are equal. So, we can find the momentum of that vehicle first whose mass and velocity is mentioned.