Question

In one dimension motion , a 1 kg object experience a force , which is function of time as F = 2t , acting . The work Dine by force in first 4 seconds is ?

Answer 1

Heya.......!!!

It's given F = 2t
Diffrentiate it
dp/dt = 2t =>> p = t^2 ( p = momentum )

Work done = Change in KE =>> p^2/2m
=»» t^4/2
at t= 4 sec
Work Done =>> 128 Joule ( J ) .


Hope it helps u

Answer 2

Answer:

The work done by 1kg object in the first 4 seconds is 128 J.

Explanation:

As per the question,

We need to find the work done by 1kg object in the first 4 seconds.

As we know, Given data is:

Mass of the object = 1 kg

Function of the force = F = 2t

As, we know,

$F = \frac{dp}{dt} \\Fdt = dp\\\int Fdt = \int dp\\\int 2t\:dt = p\\p = t^{2}$

So, we got the function of p

Now, work done = change in kinetic energy

W =Δ 1/2 mv²  = Δ p²/2m

W = (p²/2m at t=4sec - p²/2m at t=0sec)

W=(t⁴/2m at t=4sec - t⁴/2m at t=0sec)

W= 128 Joules.

Hence, The work done by 1kg object in the first 4 seconds is 128 J.

#SPJ3