- The speed, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of a train at time \(t\) seconds is given by
$$v = \sqrt { } \left( 1.2 ^ { t } - 1 \right) , \quad 0 \leqslant t \leqslant 30$$
The following table shows the speed of the train at 5 second intervals.
| \(t\) | 0 | 5 | 10 | 15 | 20 | 25 | 30 |
| \(v\) | 0 | 1.22 | 2.28 | | 6.11 | | |
- Complete the table, giving the values of \(v\) to 2 decimal places.
The distance, \(s\) metres, travelled by the train in 30 seconds is given by
$$s = \int _ { 0 } ^ { 30 } \sqrt { } \left( 1.2 ^ { t } - 1 \right) \mathrm { d } t$$
- Use the trapezium rule, with all the values from your table, to estimate the value of \(s\).
(3)