Date | May 2017 | Marks available | 1 | Reference code | 17M.2.SL.TZ1.S_7 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 1 |
Command term | Write down | Question number | S_7 | Adapted from | N/A |
Question
A particle P moves along a straight line. Its velocity vP ms−1 after t seconds is given by vP=√tsin(π2t), for 0⩽t⩽8. The following diagram shows the graph of vP.
Write down the first value of t at which P changes direction.
Find the total distance travelled by P, for 0⩽t⩽8.
A second particle Q also moves along a straight line. Its velocity, vQ ms−1 after t seconds is given by vQ=√t for 0⩽t⩽8. After k seconds Q has travelled the same total distance as P.
Find k.
Markscheme
t=2 A1 N1
[1 mark]
substitution of limits or function into formula or correct sum (A1)
eg∫80|v|dt, ∫|vQ|dt, ∫20vdt−∫42vdt+∫64vdt−∫86vdt
9.64782
distance =9.65 (metres) A1 N2
[2 marks]
correct approach (A1)
egs=∫√t, ∫k0√tdt, ∫k0|vQ|dt
correct integration (A1)
eg∫√t=23t32+c, [23x32]k0, 23k32
equating their expression to the distance travelled by their P (M1)
eg23k32=9.65, ∫k0√tdt=9.65
5.93855
5.94 (seconds) A1 N3
[4 marks]