SPM.2.SL.TZ0.6
The displacement, in centimetres, of a particle from an origin, O, at time t seconds, is given by s(t) = t 2 cos t + 2t sin t, 0 ≤ t ≤ 5.
Find the maximum distance of the particle from O.
[3]
a.
Find the acceleration of the particle at the instant it first changes direction.
[4]
b.
Markscheme / solution
use of a graph to find the coordinates of the local minimum (M1)
s = −16.513... (A1)
maximum distance is 16.5 cm (to the left of O) A1
[3 marks]
a.
attempt to find time when particle changes direction eg considering the first maximum on the graph of s or the first t – intercept on the graph of s'. (M1)
t = 1.51986... (A1)
attempt to find the gradient of s' for their value of t, s" (1.51986...) (M1)
=–8.92 (cm/s2) A1
[4 marks]
b.
Examiners’ report
[N/A]
a.
[N/A]
b.