Question

A particle moves in a straight line. Its speed(v)
increases linearly with time. If the initial speed of
the particle is vo and its speed at t = 4 s is 2V
then integration of vdt from 0 to 4 is
(1) Zvo
(3) 6v
(2) 8vo
(4) AVO​

Answer 1

Answer:

6vo.

Explanation:

From the question we get that the equation of motion v = ct + m  in which the c and m are taken as constant.

If we take that the time, t = 0 and the velocity v= vo.

Hence, we will get that the vo = m.

Therefore, substituting the values of the m in the first equation we will get that  v = ct + vo.

Now from the question we get that the time is t=4 and the velocity is v = 2vo.

Hence, we will get 2vo = c*4 + vo .

So, on solving we get that c = vo/4.

Now again on substituting the value of c in the equation we will get v = vo(t/4 + 1).

So, when we will integrate the vdt form 0 to 4 we will get (vo)integration of (t/4 + 1) which on solving from the limit 0 to 4 we will get 6vo.