9709 P41 - Jun 2010 - Q7
3783
A vehicle is moving in a straight line. The velocity \(v\) m s-1 at time \(t\) s after the vehicle starts is given by
\(v = A(t - 0.05t^2) \quad \text{for} \; 0 \leq t \leq 15,\)
\(v = \frac{B}{t^2} \quad \text{for} \; t \geq 15,\)
where \(A\) and \(B\) are constants. The distance travelled by the vehicle between \(t = 0\) and \(t = 15\) is 225 m.
- Find the value of \(A\) and show that \(B = 3375\).
- Find an expression in terms of \(t\) for the total distance travelled by the vehicle when \(t \geq 15\).
- Find the speed of the vehicle when it has travelled a total distance of 315 m.
