A body is initially moving with velocity 5 m/s and then undergoes a uniform acceleration of 2 m/s^2 for 4 seconds. What is the displacement of this body during these 4 seconds, in metres?

Introduction / Context:
Uniformly accelerated motion is a central topic in mechanics. When an object experiences constant acceleration, its displacement over a time interval can be calculated using standard kinematic equations. This question provides an initial velocity, a constant acceleration, and a time period, and asks for the displacement. Understanding how to select and apply the correct kinematic formula is essential for solving a wide variety of problems in one dimensional motion.

Given Data / Assumptions:
• Initial velocity u = 5 m/s. • Acceleration a = 2 m/s^2. • Time interval t = 4 s. • Motion is along a straight line with constant acceleration. • We are asked to find displacement s in metres.

Concept / Approach:
For uniformly accelerated motion, one useful equation for displacement is s = u * t + (1 / 2) * a * t^2. This formula combines the effect of initial velocity with the extra distance covered due to acceleration. By substituting the known values of u, a, and t into this equation, we can directly calculate the displacement. All given quantities are already in SI units, so no unit conversion is needed.

Step-by-Step Solution:
Step 1: Write the displacement formula s = u * t + (1 / 2) * a * t^2. Step 2: Substitute u = 5 m/s, a = 2 m/s^2, and t = 4 s. Step 3: Compute u * t = 5 * 4 = 20 m. Step 4: Compute t^2 = 4^2 = 16. Step 5: Compute (1 / 2) * a * t^2 = (1 / 2) * 2 * 16 = 1 * 16 = 16 m. Step 6: Add the two parts: s = 20 + 16 = 36 m.

Verification / Alternative check:
We can check consistency by first finding the final velocity and then using average velocity. Final velocity v after time t is given by v = u + a * t = 5 + 2 * 4 = 13 m/s. For uniform acceleration, the average velocity over the interval is (u + v) / 2 = (5 + 13) / 2 = 18 / 2 = 9 m/s. Displacement is average velocity times time, so s = 9 * 4 = 36 m. This matches the previous result, confirming that the calculation is correct.

Why Other Options Are Wrong:
Option a (4 m): This is far too small and would correspond to using only the acceleration part incorrectly or confusing displacement with some other quantity. Option b (72 m): This is double the correct value and may arise from forgetting the factor of 1 / 2 in the acceleration term. Option d (8 m): This again is too small and does not match either of the standard methods for calculating displacement. Option e (20 m): This is only the contribution from the initial velocity term u * t and ignores the additional displacement due to acceleration.

Common Pitfalls:
Some learners forget to include the (1 / 2) factor in the a * t^2 term, leading to an overestimated displacement. Others may mistakenly square the initial velocity or use the wrong kinematic equation. Confusing displacement with distance travelled in problems where direction changes can also cause errors, but here motion is in a single direction with positive acceleration. To avoid mistakes, always write the chosen formula clearly, substitute values step by step, and if possible verify using an alternative method.

Final Answer:
The displacement of the body in 4 seconds is 36 m.