| 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, \(v{\text{ m}}{{\text{s}}^{ - 1}}\) , at time t seconds is given by \(v = \cos ({t^2})\).
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 \( = \int_0^3 {v{\text{d}}t} \) (M1)
\( = 0.703{\text{ (m)}}\) A1
(ii) total distance \({\text{ = }}\int_0^3 {\left| v \right|{\text{d}}t} \) (M1)
\( = 2.05{\text{ (m)}}\) A1
[4 marks]
a.
solving the equation \(\int_0^t {\left| {\cos ({u^2})} \right|{\text{d}}u = 1} \) (M1)
\(t = 1.39{\text{ (s)}}\) 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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