The velocity of an object is given by the expression v(t) = 3.00 m/s + ( 4.00 m/s^3)t^2, where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time t = 0.000 s

Position of object is;

s(t) = 4t³/3 + 3t + 1

Explanation:

We are told that the velocity has an expression;

v(t) = 3.00 m/s + ( 4.00 m/s³)t²

Now, to get the expression for the position(s(t)) of the object, we have to integrate the velocity expression. Thus;

s(t) = ∫3 + 4t²

s(t) = 3t + 4t³/3 + c

Now, we were told that at x = 1.00 m, time t = 0.000 s

Thus, plugging the values in;

1 = 3(0) + 4(0³/3) + c

c = 1

Thus,the expression for the position of the object is;

s(t) = 4t³/3 + 3t + 1