| Date | November 2015 | Marks available | 3 | Reference code | 15N.2.sl.TZ0.6 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 6 | Adapted from | N/A |
Question
The velocity \(v{\text{ m}}{{\text{s}}^{ - 1}}\) of a particle after \(t\) seconds is given by
\(v(t) = {(0.3t + 0.1)^t} - 4\), for \(0 \le t \le 5\)
The following diagram shows the graph of \(v\).
Find the value of \(t\) when the particle is at rest.
[3]
a.
Find the value of \(t\) when the acceleration of the particle is \(0\).
[3]
b.
Markscheme
recognizing particle at rest when \(v = 0\) (M1)
eg\(\;\;\;{(0.3t + 0.1)^t} - 4 = 0\), \(x\)-intercept on graph of \(v\)
\(t = 4.27631\)
\(t = 4.28{\text{ }} {\text{ (seconds)}}\) A2 N3
[3 marks]
a.
valid approach to find \(t\) when \(a\) is \(0\) (M1)
eg\(\;\;\;v'(t) = 0\), \(v\) minimum
\(t = 1.19236\)
\(t = 1.19{\text{ }}{\text{ (seconds)}}\) A2 N3
[3 marks]
Total [6 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 6 - Calculus » 6.6 » Kinematic problems involving displacement \(s\), velocity \(v\) and acceleration \(a\).
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