Question

The following four graphs show four situations in which a net force acted on the same cart on a track that runs north-south. If the cart started from rest for each situation represented by the graphs, during which situation was the cart moving fastest after 8 seconds?
A)
B)
C)
D)

Answer 1

We need to find the effect of the given parameters force and time on each other to understand the resulting speeds of the same object after an equal amount of time, here, after 8 seconds. We know that the force and time gives an important property.

Complete answer:
We know that the force acting on a body over a period of time imparts an impulse on the object. The impulse is the product of the force applied and the time duration on the application of the force.
We are given a cart which is moved along the north-south direction on a track. The net force acting on the cart at every instant of time is plotted as we can see. We need to find the impulse of each case and find the one with the greatest impulse as it will be the one moving the fastest due to the impact after 8 seconds.
We know the impulse on the cart is given as the product of force and time, i.e., in our case, the area under the graphs gives us the impulse for each situation. We need to consider and compare the areas (both along north-positive and along south-negative) to find the solution to our problem.
The cart is considered to be moving north-south; therefore, a maximum positive area is required to solve this.
When we have a close comparison of the given graphs, we understand that the graph A has a greater positive area than all the others. Therefore, the cart undergoing the force pattern as in A has the greatest impulse and will be the fastest after 8 seconds.

The correct answer is option A.

Note:
The impulse is the quantity which is defined as the effect on a body subject to a force over a time interval. The momentum is the effect of velocity on the mass of a body. Both the terms have the same dimensional formulae, but have a different physical meaning.