Question
A body is moving in a straight line. When it is \(s\) metres from a fixed point O on the line its velocity, \(v\), is given by \(v = – \frac{1}{{{s^2}}},{\text{ }}s > 0\).
Find the acceleration of the body when it is 50 cm from O.
▶️Answer/Explanation
Markscheme
\(\frac{{{\text{d}}v}}{{{\text{d}}s}} = 2{s^{ – 3}}\) M1A1
Note: Award M1 for \(2{s^{ – 3}}\) and A1 for the whole expression.
\(a = v\frac{{{\text{d}}v}}{{{\text{d}}s}}\) (M1)
\(a = – \frac{1}{{{s^2}}} \times \frac{2}{{{s^3}}}\left( { = – \frac{2}{{{s^5}}}} \right)\) (A1)
when \(s = \frac{1}{2},{\text{ }}a = – \frac{2}{{{{(0.5)}^5}}}{\text{ }}( = – 64){\text{ (m}}{{\text{s}}^{ – 2}})\) M1A1
Note: M1 is for the substitution of 0.5 into their equation for acceleration.
Award M1A0 if \(s = 50\) is substituted into the correct equation.
[6 marks]