Question

What is the impulse of force shown in the following figure?

A. 205 Ns
B. 450 Ns
C. 800 Ns

Answer 1

The impulse is the force applied on the body for the short interval of time. The area under the curve in the above graph is the impulse. The area under the curve in the above graph consists of a triangle whose base is the time axis and height is the force.

Formula used:
Impulse, $I = \int {F\left( t \right)\,} dt$
where, F is the force and t is the time.

Complete step by step answer:
We know that the impulse is the force applied on the body for the short interval of time. Therefore, it is the product of force and time.
$I = F\,t$
Here, F is the force and t is the time.
For the variable force which changes with time, we can express the impulse as,
$I = \int {F\left( t \right)\,} dt$
We know that the integral is used to evaluate the area under the curve. Therefore, we can say that the impulse in the above F-t graph is the area under the curve of the F-t graph.As we can see, the area under the curve consists of a triangle whose base is the time axis and height is the force. Therefore, the area under the curve of the above graph is,
$I = \dfrac{1}{2} \times F \times \Delta t$
Here, $\Delta t$ is the interval of time for the action of force.
Substituting $F = 100\,{\text{N}}$ and $\Delta t = 10 - 1 = 9\,{\text{s}}$ in the above equation, we get,
$I = \dfrac{1}{2} \times 100 \times 9$
$\therefore I = 450\,{\text{Ns}}$
Therefore, the impulse in the above F-t graph is 450 Ns.

So, the correct answer is option B.

Note: In the given graph, note that the force is not acting on the particle till 1st second. Therefore, the interval of time for which the force is acting on the particle is 9 seconds. The impulse is also the change in momentum of the particle. Therefore, if the velocity-time graph is given, you can still calculate the impulse.