Standard +0.3 This is a straightforward M3 variable force question requiring integration of F=ma to find velocity, then solving a cubic equation. The steps are standard (apply Newton's second law, integrate with initial conditions, substitute v=2), though the arithmetic with the large coefficient 5×10³ requires care. Slightly above average difficulty due to being M3 content and requiring algebraic manipulation of the cubic.
3 A particle of mass 0.2 kg lies at rest on a smooth horizontal table. A horizontal force of magnitude \(F\) newtons acts on the particle in a constant direction for 0.1 seconds. At time \(t\) seconds,
$$F = 5 \times 10 ^ { 3 } t ^ { 2 } , \quad 0 \leqslant t \leqslant 0.1$$
Find the value of \(t\) when the speed of the particle is \(2 \mathrm {~ms} ^ { - 1 }\).
(4 marks)
3 A particle of mass 0.2 kg lies at rest on a smooth horizontal table. A horizontal force of magnitude $F$ newtons acts on the particle in a constant direction for 0.1 seconds. At time $t$ seconds,
$$F = 5 \times 10 ^ { 3 } t ^ { 2 } , \quad 0 \leqslant t \leqslant 0.1$$
Find the value of $t$ when the speed of the particle is $2 \mathrm {~ms} ^ { - 1 }$.\\
(4 marks)
\hfill \mbox{\textit{AQA M3 2008 Q3 [4]}}