Physics 2004 JAMB Past Questions - Question 12: A body of mass 4kg is acted on by a constant force of 12N for 3 seconds. The kinetic energy gained by the body at the end of the time is

Correct Answer

B

Explanation

To find the kinetic energy gained by a body when acted upon by a constant force, you can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

The work done (W) by the force (F) on the body is given by:

W = F * d

Where:
W = work done (in joules)
F = force (in newtons)
d = displacement (in meters)

In this case, the force is constant at 12N, and we need to find the work done during the 3 seconds. The formula for work done when a constant force is applied over time is:

W = F * d

But since the force is constant, we can use the formula:

W = F * d * cos(θ)

Where θ is the angle between the force and the direction of displacement. Since the force is acting in the same direction as the displacement, θ is 0 degrees, and the cosine of 0 degrees is 1. So the formula simplifies to:

W = F * d

Now, we need to calculate the displacement. In this case, we can use the formula for displacement when an object is under constant acceleration:

d = (1/2) * a * t^2

Where:
d = displacement (in meters)
a = acceleration (in meters per second squared)
t = time (in seconds)

In this case, the force applied is responsible for the acceleration, and we can use Newton's second law to find the acceleration:

F = m * a

Where:
F = force (in newtons)
m = mass (in kilograms)
a = acceleration (in meters per second squared)

Rearrange the formula for acceleration:

a = F / m

Now, plug in the values:

a = 12N / 4kg
a = 3 m/s²

Now, we can calculate the displacement:

d = (1/2) * 3 m/s² * (3 seconds)^2
d = (1/2) * 3 m/s² * 9 s²
d = 13.5 meters

Now that we have the displacement, we can calculate the work done:

W = F * d
W = 12N * 13.5m
W = 162 joules

The work done on the body is 162 joules. This is also equal to the kinetic energy gained by the body because of the work-energy theorem. So, the kinetic energy gained by the body at the end of 3 seconds is 162 joules.