the initial velocity of a particle is u (at t=0) and acceleration f is given by at.which relation is valid:

(a)v=u+at^2
(b)v=u +at^2/2
(c)v=u+at
(d)v=u

initial velocity is u

check the units. (a) and (b) are obviously false.

So, since (d) means constant velocity, (c) is the only possible choice.

V=u at^2

C us correct dear

To find the valid relation between the initial velocity (u), acceleration (a), and time (t), we can use the equations of motion.

The equations of motion for a particle with constant acceleration are as follows:

1. v = u + at
2. s = ut + (1/2)at^2
3. v^2 = u^2 + 2as

Let's go through each option and see which one matches these equations.

Option (a): v = u + at^2
This equation is not valid because the term 'at^2' is incorrect. The correct term would be 'at' without squaring.

Option (b): v = u + at^2/2
This equation is also not valid because the term 'at^2/2' is incorrect. The correct term would be 'at', not divided by 2.

Option (c): v = u + at
This equation is valid. It matches the first equation of motion, where the final velocity (v) is equal to the initial velocity (u) plus the product of acceleration (a) and time (t).

Option (d): v = u
This equation is not valid. It ignores the effect of acceleration and suggests that the final velocity is the same as the initial velocity, which is not the case when acceleration is present.

Therefore, the correct relation is (c) v = u + at.