1.

a force is acting on a mass of 6kg displacement x of the mass is related to time t as x=t2/4 meter.work done by the force in 2 sec is

Answer»

Given,
Mass of body , m = 6 kg
displacement is the function of TIME , x = t²/4
∵ Workdone = force × displacement , but here no any external force ACT on body.
∴ we have to use ,
Workdone = Change in KINETIC energy

Now, x = t²/4
differentiate x with respect to time ,
dx/dt = 2t/2 = t/2
We know, dx/dt = velocity of body
At t = 2sec, velocity of body , v = 2/2 = 1 m/s
So, change in kinetic energy = final kinetic energy - intial kinetic energy of body
= 1/2mv² - 0 [because initially body is in rest because velocity of body at t = 0, is 0 ]
∴ change in kinetic energy = 1/2 × 6 × (1)²
= 1/2 × 6 = 3 J

Hence , Workdone = 3J



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