Question

Which equation best describes velocity time relation

Answer 1

v = ds/dt
s = displacement 
t = time

v = time rate of change in the displacement.

Answer 2

Equation for Velocity-Time Relation

Consider the velocity-time graph of an object that moves under uniform acceleration as shown in Fig. 8 (similar to Fig. 6, but now with u ≠ 0). From this graph, you can see that initial velocity of the object is u (at point A) and then it increases to v (at point B) in time t. The velocity changes at a uniform rate a. In Fig. 8, the perpendicular lines BC and BE are drawn from point B on the time and the velocity axes respectively, so that the initial velocity is represented by OA, the final velocity is represented by BC and the time interval t is represented by OC. BD = BC – CD, represents the change in velocity in time interval t.

Let us draw AD parallel to OC. From the graph, we observe that
BC = BD + DC = BD + OA
Substituting BC = v and OA = u,
We getv = BD + u
OrBD = v – u(8)
From the velocity-time graph (Fig. 8), the acceleration of the object is given by

Substituting OC = t, we get
a = BD/t
OrBD = at(9)
Using Eqs. (8) and (9) we get
v = u + at
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