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A body of mass 6 kg is acted upon by a force which causes a displacement in it given x = t2/4 metre where   t  is the time in second. The work done by the force in 2 seconds is
  • a)
    12 J
  • b)
    9J
  • c)
    6 J
  • d)
    3 J
Correct answer is option 'D'. Can you explain this answer?
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A body of mass 6 kg is acted upon by a force which causes a displaceme...
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A body of mass 6 kg is acted upon by a force which causes a displaceme...

Explanation:

Given data:
- Mass of the body (m) = 6 kg
- Displacement (x) = t^2/4 meters
- Time (t) = 2 seconds

Formula for work done:
Work done (W) = Force (F) * Displacement (x)

Calculating displacement:
Given x = t^2/4
Substitute t = 2 seconds
x = (2)^2 / 4
x = 4 / 4
x = 1 meter

Calculating force:
Since Force (F) = mass (m) * acceleration (a)
Acceleration (a) = Change in velocity / time taken
Here, velocity (v) = dx/dt
Given x = t^2/4, differentiate with respect to t to find velocity
v = d(t^2/4)/dt
v = (2t) / 4
v = t / 2

Now, acceleration a = dv/dt
a = d(t/2)/dt
a = (1/2)

F = m * a
F = 6 * (1/2)
F = 3 N

Calculating work done:
Work done (W) = F * x
W = 3 * 1
W = 3 Joules

Therefore, the work done by the force in 2 seconds is 3 Joules, which corresponds to option 'D'.
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