Difficulty: Medium
Correct Answer: 50 joule
Explanation:
Introduction / Context:
Work and kinetic energy are closely related in mechanics. When a net force acts on a body and changes its speed, the work done by that force is equal to the change in the kinetic energy of the body. This question uses that relationship to find the work done when a body is accelerated from rest to a certain speed.
Given Data / Assumptions:
Concept / Approach:
The work energy theorem states that the net work done on an object equals the change in its kinetic energy. Mathematically, W = KE final minus KE initial. Kinetic energy is given by KE = (1 / 2) * m * v^2. Using the initial and final velocities, we can calculate the change in kinetic energy and thus the work done by the force.
Step-by-Step Solution:
Verification / Alternative check:
The answer can be checked by estimating. A 4 kilogram mass moving at 5 metre per second is not extremely fast, so an energy of tens of joule is reasonable. The calculation 0.5 * 4 * 25 naturally gives 50, so the arithmetic is straightforward and consistent.
Why Other Options Are Wrong:
Option B: 30 joule does not match the computed change in kinetic energy and likely arises from a random mistake.
Option C: 20 joule could result from using an incorrect formula such as m * v instead of (1 / 2) * m * v^2.
Option D: 40 joule might come from miscalculating 0.5 * 4 * 5^2 as 40 instead of 50, showing a multiplication error.
Common Pitfalls:
Students sometimes forget that work depends on change in kinetic energy, not just on final energy. Others may incorrectly square the velocity or misplace decimal points. Keeping the formula W = (1 / 2) * m * v^2 minus (1 / 2) * m * u^2 in mind and performing each step carefully helps avoid such mistakes.
Final Answer:
The work done by the force on the body is 50 joule.
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