Higher November 2017 Paper 5 Q13

OCRHigherCurrent spec10 marksDrawing & Using Graphs

13 The graph shows information about the speed of a vehicle during the final 50 seconds of a journey.
At the start of the 50 seconds the speed is \(k\) metres per second.
The distance travelled during the 50 seconds is 1.35 kilometres.

Speed-time graph: time from 0 to 50 seconds across, speed in m/s up with only k marked; horizontal line at speed k from 0 to 40 seconds, then a straight line down to 0 at 50 seconds

(a) Work out the average speed of the vehicle during the 50 seconds.
Give your answer in metres per second.

........................................ m/s [2]

(b) Work out the value of \(k\). [5]

(c)

(i) Calculate the gradient of the graph in the final 10 seconds of the journey. [1]

(ii) Describe what this gradient represents. [2]

Answer	Marks	Part marks and guidance
27	2	M1 for 1350 ÷ 50 If 0 scored SC1 for answer figs 27

Mark scheme (b)

Answer	Marks	Part marks and guidance
30	5	B1 for 1350 M3 for 1350 = 40\(k\) + ½ ×10×\(k\) oe or M2 for 40\(k\) + ½ ×10×\(k\) oe or M1 for any attempt to find any relevant area under the graph	Condone figs 135 for M3 and variable other than \(k\)

Answer	Marks	Part marks and guidance
(i) –3	1FT	FT (–their (b) ÷ 10)
(ii) [Constant] deceleration oe	1		Condone acceleration The rate at which the speed changes
m/s\(^2\)	1