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]