Date | May 2021 | Marks available | 2 | Reference code | 21M.1.SL.TZ2.9 |
Level | Standard Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 2 |
Command term | Find | Question number | 9 | Adapted from | N/A |
Question
Particle A travels in a straight line such that its displacement, metres, from a fixed origin after seconds is given by , for , as shown in the following diagram.
Particle A starts at the origin and passes through the origin again when .
Particle A changes direction when .
The total distance travelled by particle A is given by .
Find the value of .
Find the value of .
Find the displacement of particle A from the origin when .
Find the distance of particle A from the origin when .
Find the value of .
A second particle, particle B, travels along the same straight line such that its velocity is given by , for .
When , the distance travelled by particle B is equal to .
Find the value of .
Markscheme
setting (M1)
(accept ) A1
Note: Award A0 if the candidate’s final answer includes additional solutions (such as ).
[2 marks]
recognition that when particle changes direction OR local maximum on graph of OR vertex of parabola (M1)
(accept ) A1
[2 marks]
substituting their value of into OR integrating from to (M1)
A1
[2 marks]
OR OR integrating from to (M1)
A1
[2 marks]
forward backward OR OR (M1)
A1
[2 marks]
METHOD 1
graphical method with triangles on graph M1
(A1)
(A1)
A1
METHOD 2
recognition that distance M1
(A1)
(A1)
A1
[4 marks]