| Date | None Specimen | Marks available | 4 | Reference code | SPNone.2.hl.TZ0.5 |
| Level | HL only | Paper | 2 | Time zone | TZ0 |
| Command term | Calculate | Question number | 5 | Adapted from | N/A |
Question
The particle P moves along the x-axis such that its velocity, v ms−1 , at time t seconds is given by v=cos(t2).
Given that P is at the origin O at time t = 0 , calculate
(i) the displacement of P from O after 3 seconds;
(ii) the total distance travelled by P in the first 3 seconds.
[4]
a.
Find the time at which the total distance travelled by P is 1 m.
[2]
b.
Markscheme
(i) displacement =∫30vdt (M1)
=0.703 (m) A1
(ii) total distance = ∫30|v|dt (M1)
=2.05 (m) A1
[4 marks]
a.
solving the equation ∫t0|cos(u2)|du=1 (M1)
t=1.39 (s) A1
[2 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 6 - Core: Calculus » 6.6 » Kinematic problems involving displacement s, velocity v and acceleration a.
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