Question

4. A particle of mass 3 kg is moving along X-axis and its position at time t is given by equation x = (2t square+ 5) m.
Work done by all the forces acting on it in time interval t = 0 to t = 3 s is
(1) 144 J
(2) 72 J
(3) 108 J
(4) 216 J​

Answer 1

Mass (m) = 3 kg.

Position at time t,

x = 2t² + 5

At t = 0, the body is at, from the equation

x = 2(0)² + 5 = 5 units.

At t = 3, from the equation, the body is at,

x = 2(3)² + 5 = 23 units.

We can say, Displacement in t= 0 to t = 3 seconds, is 23 – 5 = 18 m.

Now let's take another time interval of 3 seconds from t = 3 to t = 6

For t = 6, it covers distance of 2(6)² + 5 = 72 + 5 = 77.

Distance in this particular 3 seconds can be taken as 77 - 23 = 55 m.

Therefore the body is accelerating.

Now, Since we aren't aware of its velocities . All we can do is to differentiate the equation twice w.r.t time.

s = 2t² + 5 ⇒ds/dt = 2(2t) ⇒v = 4t ⇒Now, dv/dt = 4(1)(t^0)=4(1)(1)

⇒ a = 4 m/s²

Now,

We have Time t = 3 seconds ( from t=0 to t=3)

Mass of the body is 3 Kg.

Acceleration is 4m/s²

Displacement in the t=0 to t=3 is 18 m.

Work done = mas =3(4)(18) = 216 J.