Question

Suppose a mass m is moving along a straight line with some initial velocity u. It is uniformly accelerated to velocity v, in the time t by the application of constant non-zero force F. The correct relationship between F, v, u and t can be

Answer 1

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Answer 2

The initial velocity of the body is given as u .

The final velocity of the body is given as v.

The mass of the body is given as m .

The body is acted upon by a constant non zero force F.

The momentum of a body is defined as the product of mass with velocity.

Mathematically momentum p = mv.

The initial momentum of the body p = m×u

The final momentum of the body p' = m×v

The change in momentum dp = p' - p

                                                  = mv - mu

                                                  = m ( v- u)

The time taken by the body is t .

From Newton's second law, we know that rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

Mathematically it can be written as  $\frac{dp}{dt} =\ F$

                                                          ⇒ $\frac{m(v-u)}{t} =\ F$

                                                           $i.e\ F=\frac{m(v-u)}{t}$

This is the required expression among F, u, v and t respectively.