Question

The velocity of a particle moving in a straight line is given by the following formula.
v(t) = t*2 + 3
Given that s = 6 at time t = 0 Find an expression for s in terms of t without any unknown constants.
s(t)=?

Answer 1

Velocity is the derivative of position (the change in position over time). Therefore if we integrate the equation for velocity we will have an equation for position.
\[s(t)=\int{(t^2+3)}dt = \frac{t^3}{3}+3t+C\]
But we need to solve for C. We know that at t=0, s = 6 so C must be:
\[s(0)=\frac{0^3}{3}+3*0+C=6=0+0+6=6\] Hence:
\[s(t)=\frac{t^3}{3}+3t+6\]