C2 January 2006 Q6

EdexcelOld spec6 marksIntegration

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.

\(t\)	0	5	10	15	20	25	30
\(v\)	0	1.22	2.28		6.11

(a) Complete the table, giving the values of \(v\) to 2 decimal places. (3)

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

(b) Use the trapezium rule, with all the values from your table, to estimate the value of \(s\). (3)

Mark scheme (a)

\(t\)	0	5	10	15	20	25	30
\(v\)	0	1.22	2.28	3.80	6.11	9.72	15.37

Scheme	Marks
\(t = 15 \quad 25 \quad 30\) \(v = \underline{3.80} \quad \underline{9.72} \quad \underline{15.37}\)	B1 B1 B1
	(3)

S.C. Penalise AWRT these values once at first offence, thus the following marks could be AWRT 2 dp (Max 2/3)