Determine the first time t₁ at which P has zero velocity.

Find an expression for the acceleration of P at time t.

Find the value of the acceleration of P at time t₁.

attempt to solve $v\left( t \right) = 0$ for t or equivalent     (M1)

t₁ = 0.441(s)     A1

[2 marks]

$a\left( t \right) = \frac{{{\text{d}}v}}{{{\text{d}}t}} =  - {{\text{e}}^{ - t}} - 16t{{\text{e}}^{ - 2t}} + 16{t^2}{{\text{e}}^{ - 2t}}$      M1A1

Note: Award M1 for attempting to differentiate using the product rule.

[2 marks]

$a\left( {{t_1}} \right) =  - 2.28$ (ms⁻²)      A1

[1 mark]