A car of mass 1200 kg decelerates from \(30 \mathrm {~ms} ^ { - 1 }\) to \(20 \mathrm {~ms} ^ { - 1 }\) in 6 seconds at a constant rate.
- Find the magnitude, in N , of the decelerating force.
- Find the loss, in J , in the car's kinetic energy.
- A particle moves in a straight line from \(A\) to \(B\) in 5 seconds. At time \(t\) seconds after leaving \(A\), the velocity of the particle is \(\left( 32 t - 3 t ^ { 2 } \right) \mathrm { ms } ^ { - 1 }\).
- Calculate the straight-line distance \(A B\).
- Find the acceleration of the particle when \(t = 3\).
- Eddie, whose mass is 71 kg , rides a bicycle of mass 25 kg up a hill inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 12 }\). When Eddie is working at a rate of 600 W , he is moving at a constant speed of \(6 \mathrm {~ms} ^ { - 1 }\).
Find the magnitude of the non-gravitational resistance to his motion. - A boat leaves the point \(O\) and moves such that, \(t\) seconds later, its position vector relative to \(O\) is \(\left( t ^ { 2 } - 2 \right) \mathbf { i } + 2 t \mathbf { j }\), where the vectors \(\mathbf { i }\) and \(\mathbf { j }\) both have magnitude 1 metre and are directed parallel and perpendicular to the shoreline through \(O\).
- Find the speed with which the boat leaves \(O\).
- Show that the boat has constant acceleration and state the magnitude of this acceleration.
- Find the value of \(t\) when the boat is 40 m from \(O\).
- Comment on the limitations of the given model of the boat's motion.
\includegraphics[max width=\textwidth, alt={}]{996976f3-2a97-4c68-8c97-f15a3bfde9a2-1_446_595_1965_349}
The diagram shows a body which may be modelled as a uniform lamina.
The body is suspended from the point marked \(A\) and rests in equilibrium.