M1 June 2006 Q1

EdexcelOld spec6 marksTime-Series Graphs

Figure 1: speed-time graph rising in a straight line from 2 at t = 0 to 5 at t = 3, then constant at 5 until t = 7 — Figure 1

Figure 1 shows the speed-time graph of a cyclist moving on a straight road over a 7 s period. The sections of the graph from \(t = 0\) to \(t = 3\), and from \(t = 3\) to \(t = 7\), are straight lines. The section from \(t = 3\) to \(t = 7\) is parallel to the \(t\)-axis.

State what can be deduced about the motion of the cyclist from the fact that

(a) the graph from \(t = 0\) to \(t = 3\) is a straight line, (1)

(b) the graph from \(t = 3\) to \(t = 7\) is parallel to the \(t\)-axis. (1)

Mark scheme (a)

Scheme	Marks
Constant acceleration	B1
	(1)

Notes

(a) and (b) Accept ‘steady’ instead of ‘constant. Allow ‘o.e.’ (= ‘or equivalent’) within reason! But must have idea of constant.

‘constant speed and constant acceleration’ for (a) or (b) is B0

Mark scheme (b)

Scheme	Marks
Constant speed/velocity	B1
	(1)

Notes

(a) and (b) Accept ‘steady’ instead of ‘constant. Allow ‘o.e.’ (= ‘or equivalent’) within reason! But must have idea of constant.

‘constant speed and constant acceleration’ for (a) or (b) is B0

Mark scheme (c)

Scheme	Marks
Distance \(= \tfrac{1}{2}(2 + 5) \times 3,\ + (4 \times 5)\)	M1 A1, B1
\(= 30.5\) m	A1
	(4)
	(6 marks)

Notes

(c) M1 for valid attempt at area of this trap. as area of a trap. Or this trap. as = triangle + rectangle, i.e. correct formula used with at most a slip in numbers.

B1 for area of rectangle as \(5 \times 4\)

Treating whole as a single const acceln situation, or whole as a single trapezium, is M0.

If assume that top speed is 5.1 or 5.2, allow full marks on f.t. basis (but must be consistent)