M1 January 2005 Q3

EdexcelOld spec9 marksTime-Series Graphs

Figure 2: speed-time graph rising from O to 9 at t = 4, constant to t = 20, then falling to u at t = 25 — Figure 2

A sprinter runs a race of 200 m. Her total time for running the race is 25 s. Figure 2 is a sketch of the speed-time graph for the motion of the sprinter. She starts from rest and accelerates uniformly to a speed of 9 m s\(^{-1}\) in 4 s. The speed of 9 m s\(^{-1}\) is maintained for 16 s and she then decelerates uniformly to a speed of \(u\) m s\(^{-1}\) at the end of the race. Calculate

(a) the distance covered by the sprinter in the first 20 s of the race, (2)

(b) the value of \(u\), (4)

Scheme	Marks
Distance \(= \tfrac{1}{2} \times 4 \times 9 + 16 \times 9\) or \(\tfrac{1}{2}(20 + 16) \times 9\)	M1
\(= 162\) m	A1
	(2)

Scheme	Marks
Distance over last 5 s \(= \tfrac{1}{2}(9 + u) \times 5\)	M1
\(162 + \tfrac{1}{2}(9 + u) \times 5 = 200\)	M1 A1ft
\(\Rightarrow u = 6.2\) m s\(^{-1}\)	A1
	(4)

Scheme	Marks
\(6.2 = 9 + 5a\)	M1 A1ft
\(a = (-)\,0.56\) m s\(^{-2}\)	A1
	(3)
	(9 marks)