Physics, asked by anjlikukreja329, 8 months ago

a ball of mass 2 kg moves so that its position x as function of time t is given by x=t³/3 if x is measured in metres and 't' in seconds,what is the kinetic energy acquired by the particle in first two seconds ..?


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Answers

Answered by SURYANSHDIXIT
14

Position of the body varies as x=t^3\3

Thus the acceleration of the body at any instant=d^2x\dt^2=2t

Force any on body at any instant=ma=2mt

Thus work done on body in moving the object by a distance dx=F.dx=2mtdx

=2mt(t^2dt)

Thus total work done in 2s=∫ 0^2 2mt^3dt

                                          =16J

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Answered by DrNykterstein
25

Answer :-

16 joule

Explanation :-

We are given,

  • Mass of a ball, m = 2 kg
  • Position of the ball is given as a function of time : x = / 3

We have to find the kinetic energy acquired by the body in first two seconds.

But position is given as a function of time, so we differentiate it with respect to t to get velocity as a function of time.

⇒ x = t³ / 3

⇒ dx / dt = d(t³ / 3) / dt

⇒ v = 1/3 × 3 × t²

v =

Let us find the velocity at t = 0

⇒ v = (0)² => v = 0

We get to know that the ball was at rest at time t = 0, Now let us find the velocity of the ball after 2 seconds.

⇒ v = (2)²

v = 4 m/s [ x in meters, t in seconds]

Now, Let us find the kinetic energy acquired by the ball in two seconds.

⇒ KE = 1/2 (mv²)

⇒ KE = 1/2 × 2 × (4)²

⇒ KE = 4²

KE = 16 joule

Hence, The kinetic energy acquired by the body in two seconds is 16 joule.

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