Question

A motion of a particle is given by the relationship a=6t. If s=8m and v=4m/s when t=1sec determine:

a) v-s relationship
b) s-t relationship

s is distance
V is velocity
T is time

Answer 1

a) v-s relationship is v = ds/dt. Did you mean to say v-t relationship? If so that is:
v = ∫ a dt
v = ∫ (6t) dt
v = 3t^2 + c
4 = 3(1)^2 + c
c = 1
v = 3t^2 + 1

b) s = ∫ v dt
s = ∫ (3t^2 + 1) dt
Continue similarly to a) above.