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Date November 2017 Marks available 5 Reference code 17N.1.hl.TZ0.5
Level HL only Paper 1 Time zone TZ0
Command term Find Question number 5 Adapted from N/A

Question

A particle moves in a straight line such that at time t seconds (t, its velocity v, in {\text{m}}{{\text{s}}^{ - 1}}, is given by v = 10t{{\text{e}}^{ - 2t}}. Find the exact distance travelled by the particle in the first half-second.

Markscheme

s = \int\limits_0^{\frac{1}{2}} {10t{{\text{e}}^{ - 2t}}{\text{d}}t}

attempt at integration by parts     M1

= \left[ { - 5t{{\text{e}}^{ - 2t}}} \right]_0^{\frac{1}{2}} - \int\limits_0^{\frac{1}{2}} { - 5{{\text{e}}^{ - 2t}}{\text{d}}t}     A1

= \left[ { - 5t{{\text{e}}^{ - 2t}} - \frac{5}{2}{{\text{e}}^{ - 2t}}} \right]_0^{\frac{1}{2}}     (A1)

 

Note:     Condone absence of limits (or incorrect limits) and missing factor of 10 up to this point.

 

s = \int\limits_0^{\frac{1}{2}} {10t{{\text{e}}^{ - 2t}}{\text{d}}t}     (M1)

=  - 5{{\text{e}}^{ - 1}} + \frac{5}{2}{\text{ }}\left( { = \frac{{ - 5}}{{\text{e}}} + \frac{5}{2}} \right){\text{ }}\left( { = \frac{{5{\text{e}} - 10}}{{2{\text{e}}}}} \right)     A1

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 6 - Core: Calculus » 6.6 » Kinematic problems involving displacement s, velocity v and acceleration a.
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