C2 January 2006 Q6

6. The speed, \(v\) m s^–1, of a train at time \(t\) seconds is given by\[v = \sqrt{(1.2^t - 1)}, \quad 0 \leqslant t \leqslant 30.\]

The following table shows the speed of the train at 5 second intervals.

The distance, \(s\) metres, travelled by the train in 30 seconds is given by\[s = \int_0^{30} \sqrt{(1.2^t - 1)}\,\mathrm{d}t.\]