Question

A jeep carries a trailer on a level road at a constant speed of 10m/s. Calculate the power exerted on the trailer if the tension in the coupling is 2000N.
$A.{\text{ 20kW}} \\\ {\text{B. 30kW}} \\\ {\text{C. 40kW}} \\\ {\text{D. 50kW}} \\\$

Answer 1

Hint- Here we will proceed by using the formula of power i.e.$P = \dfrac{W}{T}$ where W is replaced by formula of work done i.e. $W = F \times D$. Then substitute the given values of tension i.e. 2000N and velocity i.e. 10m/s to get the required result.
Formula used-
$P = \dfrac{W}{T}$
$W = F \times D$
$P = F \times V$

Complete step-by-step answer:

Here we are given that-
Tension = 2000N
Speed of jeep, Velocity = 10m/s
Now we will find the power exerted on the trailer.
As we know that the energy per unit time is called power exerted on the trailer or power is the rate at which work is done, the rate at which energy is consumed.
It is given by-
$P = \dfrac{W}{T}$
Where W is work done i.e. it is calculated by multiplying the force by the amount of movement of an object.
T is time
Also, we know that work done is the product of force and displacement.
$\Rightarrow W = F \times D$
Where F is force i.e. It is the external object motion or tends to produce motion or it stops motion or tends to stop motion.
And D is displacement i.e. the object’s overall change in position.
So, we can say that-
$P = F \times V$
Now substituting the values of f and v in the formula-
$P = 2000N \times 10m/s$
$P = 20kW$
Therefore, we conclude that if the tension in the coupling is 2000N,
The power exerted on the trailer is 20kW.
Hence, option A is correct.

Note- While solving this question, we should make sure that we put the SI unit along with the answer as here kw (kilowatts) is the SI unit of power. Also one must know that there is also other way to write the formula of power i.e. $P = \dfrac{E}{T}$where E is energy and T is time.