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.

$\frac{{{\text{d}}v}}{{{\text{d}}s}} = 2{s^{ - 3}}$     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]