A body of mass 5 kg accelerates uniformly from 12 m/s to 20 m/s in 4 seconds due to a constant net force. What is the magnitude of this force (in newtons)?

Introduction / Context:
This problem uses Newton second law of motion, which relates the net force acting on a body to the product of its mass and acceleration. The body speed changes from 12 m/s to 20 m/s over a specified time interval, so we can find its acceleration and then determine the force causing this acceleration. It is a straightforward application of kinematics and dynamics.

Given Data / Assumptions:

• Mass of the body, m = 5 kg.
• Initial velocity, u = 12 m/s.
• Final velocity, v = 20 m/s.
• Time interval, t = 4 s.
• The net force is constant, producing uniform acceleration.
• Motion is along a straight line.

Concept / Approach:
Acceleration a is defined as the rate of change of velocity, a = (v - u) / t. Once we compute acceleration, we apply Newton second law, F = m * a, to find the net force. Careful substitution and correct units are crucial. Since all values are small and neat, the arithmetic should be manageable, but attention must still be paid to the correct formula and order of operations.

Step-by-Step Solution:
Step 1: Compute the change in velocity: v - u = 20 m/s - 12 m/s = 8 m/s. Step 2: Use the definition of acceleration: a = (v - u) / t = 8 m/s / 4 s = 2 m/s^2. Step 3: Apply Newton second law: F = m * a. Step 4: Substitute the mass and acceleration: F = 5 kg * 2 m/s^2. Step 5: Multiply to get F = 10 kg·m/s^2. Step 6: Recognise that 1 kg·m/s^2 is 1 newton, so F = 10 N.

Verification / Alternative check:
As a quick check, note that the acceleration is modest (2 m/s^2), and the mass is 5 kg, so a force of 10 N is reasonable. If you recompute acceleration with the numbers swapped or misread the time as 2 s, you would get different accelerations and forces, which would not match both the given velocities and time. Rechecking the arithmetic confirms the correctness of 2 m/s^2 and 10 N.

Why Other Options Are Wrong:
40 N: This would correspond to an acceleration of 8 m/s^2 for a 5 kg mass, which is inconsistent with the given change in velocity over 4 seconds.

20 N: This would correspond to an acceleration of 4 m/s^2, which would change velocity by 16 m/s in 4 seconds, not by 8 m/s.

80 N: This is far too large for the given rate of change of velocity and would imply an acceleration of 16 m/s^2, again inconsistent with the data.

Common Pitfalls:
Students sometimes plug values into the wrong kinematic formula or forget whether to subtract u from v or vice versa. Always remember that acceleration is (final velocity minus initial velocity) divided by time, and then apply F = m * a. Keeping units visible at each step helps avoid mixing up time and velocity or forgetting to square units where needed.

Final Answer:
The magnitude of the force acting on the body is 10 N.