Question

A particle moves with a fixed acceleration 3 m/s^2. If its initial velocity is s(0)=0:
a) Find its velocity function.

b) How long does it take for the particle to reach the velocity 14 m/s^2?

c) Find the distance the particle traveled when its velocity reaches 14 m/s^2.

Answer 1

a(t) = 3
v(t) = 3t + c, where c is a constant

(you say, "If its initial velocity is s(0) = 0 "
did you mean v(0) = 0 ?
usually s(t) is used for distance and
v(t) is used for velocity
I will assume you meant v(0) = 0 )

v(0) = 0 + c ---> c = 0

a) v(t) = 3t

b) so 3t = 14
t = 14/3 seconds

c) s(t) = (3/2)t^2 + k , where k is a constant
assuming that the particle started from a zero position, k=0
then when t = 4/3
s(4/3) = (3/2)(16/9) = 19/6 m