Motion, forces and energy：練習問題

The diagram shows a speed–time graph for a moving object. The graph is a straight line starting from the origin with a constant positive gradient.
What does the gradient of this graph represent?

A constant force of \( 50\text{ N} \) is used to push a box a distance of \( 4\text{ m} \) across a level floor.
How much work is done on the box?

A crane lifts a load of \(250\text{ kg}\) to a vertical height of \(12\text{ m}\) in \(20\text{ seconds}\). The total electrical power input to the crane is \(2.5\text{ kW}\).
What is the efficiency of the crane? [Use \(g = 9.8\text{ N/kg}\)]

Which statement correctly describes the weight of an object?

A car of mass \(1200\text{ kg}\) is accelerating along a straight road. The engine provides a forward driving force of \(4000\text{ N}\) and the total resistive force is \(1600\text{ N}\).
What is the acceleration of the car?

An object has a mass of \(25\text{ kg}\). Calculate the weight of this object on Earth, given that the gravitational field strength \(g\) is approximately \(9.8\text{ N/kg}\).

A cyclist travels a total distance of \(4.5\text{ km}\) in a time of \(15\text{ minutes}\). Calculate the average speed of the cyclist in \(\text{m/s}\).

The diagram shows a speed–time graph for a vehicle of mass \(1500\text{ kg}\) being tested on a straight track. The vehicle accelerates uniformly from rest to a speed of \(30\text{ m/s}\) in \(4.0\text{ s}\), and then continues at this constant speed for the remaining \(6.0\text{ s}\).
(a) Calculate the acceleration of the vehicle during the first \(4.0\text{ s}\).
(b) Determine the total distance travelled by the vehicle during the entire \(10.0\text{ s}\) test.
(c) Calculate the kinetic energy of the vehicle when it has reached its constant speed of \(30\text{ m/s}\).
(d) While moving at the constant speed of \(30\text{ m/s}\), the vehicle overcomes a total resistive force of \(850\text{ N}\). Calculate the power developed by the motor during this constant speed phase.
(e) During the first \(4.0\text{ s}\), the motor is supplied with \(7.5 \times 10^5\text{ J}\) of electrical energy. Calculate the percentage efficiency of the motor in converting this electrical energy into kinetic energy during the acceleration phase.