Standard +0.3 This is a straightforward M3 variable force question requiring application of F=ma with a time-dependent force, integration to find velocity, and solving a quadratic equation. The setup is clear, the integration is routine (polynomial), and the method is standard textbook procedure. Slightly easier than average due to the direct application of a well-practiced technique with no conceptual obstacles.
1 A stone, of mass 2 kg , is moving in a straight line on a smooth horizontal sheet of ice under the action of a single force which acts in the direction of motion. At time \(t\) seconds, the force has magnitude \(( 3 t + 1 )\) newtons, \(0 \leqslant t \leqslant 3\).
When \(t = 0\), the stone has velocity \(1 \mathrm {~ms} ^ { - 1 }\).
When \(t = T\), the stone has velocity \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Find the value of \(T\).
(6 marks)
1 A stone, of mass 2 kg , is moving in a straight line on a smooth horizontal sheet of ice under the action of a single force which acts in the direction of motion. At time $t$ seconds, the force has magnitude $( 3 t + 1 )$ newtons, $0 \leqslant t \leqslant 3$.
When $t = 0$, the stone has velocity $1 \mathrm {~ms} ^ { - 1 }$.\\
When $t = T$, the stone has velocity $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
Find the value of $T$.\\
(6 marks)
\hfill \mbox{\textit{AQA M3 2013 Q1 [6]}}