Three particles of masses \(2 \mathrm {~kg} , 3 \mathrm {~kg}\) and \(m \mathrm {~kg}\) are positioned at the points with coordinates \(( a , 3 ) , ( 3 , - 1 )\) and \(( - 2,4 )\) respectively. Given that the centre of mass of the particles is at the point with coordinates \(( 0,2 )\), find
the value of \(m\),
the value of \(a\).
A car has mass 1200 kg . The maximum power of the car's engine is 32 kW . The resistance to motion due to non-gravitational forces is modelled as a force of constant magnitude 800 N . When the car is travelling on a horizontal road at constant speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the engine of the car is working at maximum power.
Find the value of \(V\).
The car now travels downhill on a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 40 }\). The resistance to motion due to non-gravitational forces is still modelled as a force of constant magnitude 800 N . Given that the engine of the car is again working at maximum power,
find the acceleration of the car when its speed is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).