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Numeracy Higher June 2017 Unit 1 Q10

WJECHigherCurrent spec13 marksCompound MeasuresDrawing & Using GraphsRecurring Decimals

10. The graph below shows a 120-second section of Iestyn’s car journey to work this morning.

Speed (metres per second, 0 to 35) against Time, t (seconds, 0 to 120). Curve starts at 10, rises to about 15 by t = 15 to 20, rises steeply to 25 at t = 40, levels off at 30 from t = 60, small dip near t = 75 and bump near t = 85, stays at 30 until about t = 118, then drops sharply to 15 at t = 120
(a)
(i) At \(t\) = 50 seconds, estimate the acceleration of Iestyn’s car in m/s2.
Leave your answer as a fraction. [3]
(ii) At another time, Iestyn calculated the acceleration of the car to be \(0{\cdot}2\dot{4}\) m/s2.
Write this recurring decimal as a fraction. [2]
(b)
(i) Calculate an estimate of the distance travelled by Iestyn’s car in the first 80 seconds of his journey.
You must consider the speed of the car when \(t\) = 0, 20, 40, 60 and 80 seconds. [4]
(ii) Hence, calculate an estimate of the average speed of Iestyn’s car for this entire 120-second section of his car journey.
Give your answer in m/s. [4]
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