Forces and motion：練習問題

An astronaut has a mass of \( 75\text{ kg} \) on Earth. If the gravitational field strength on the Moon is \( 1.6\text{ N/kg} \), what is the astronaut's weight on the Moon?

A wooden block with a mass of \( 4.0\text{ kg} \) is pushed along a horizontal surface with a constant force of \( 20\text{ N} \). If the block accelerates at \( 3.5\text{ m/s}^2 \), what is the magnitude of the frictional force opposing the motion?

A car travels along a straight road. Its velocity increases from \( 12\text{ m/s} \) to \( 27\text{ m/s} \) over a period of \( 5.0\text{ s} \). What is the acceleration of the car?

A stone is dropped from the top of a cliff and hits the water below with a speed of \( 22\text{ m/s} \). Taking \( g = 10\text{ m/s}^2 \) and ignoring air resistance, calculate the height of the cliff.

A car accelerates from rest at a constant rate of \(2.5\text{ m/s}^2\). Calculate the distance the car travels while reaching a speed of \(20\text{ m/s}\).

The following velocity-time graph represents the motion of a cyclist. Calculate the acceleration of the cyclist during the first \(8.0\text{ s}\) if their velocity increases from \(0\) to \(12\text{ m/s}\) at a constant rate.

A car of mass \(1200\text{ kg}\) is accelerating along a flat road. The engine provides a forward driving force of \(3500\text{ N}\), while the total resistive force acting on the car is \(1100\text{ N}\). Calculate the acceleration of the car.

A small object is dropped from a stationary helicopter at a height of \(45\text{ m}\) above the ground. Ignoring air resistance and taking \(g = 10\text{ m/s}^2\), calculate the speed at which the object hits the ground.

A cyclist starts from rest and accelerates uniformly at \(1.5\text{ m/s}^2\) for \(6\text{ seconds}\). They then continue at a constant velocity for a further \(20\text{ seconds}\).

(a) Calculate the final velocity of the cyclist after the first \(6\text{ seconds}\).
(b) Determine the total distance traveled by the cyclist during the entire \(26\text{ second}\) journey. Hint: Consider the area under a velocity-time graph.

A skydiver with a mass of \(75\text{ kg}\) jumps out of a stationary balloon. Take \(g = 10\text{ m/s}^2\).

(a) Describe the motion of the skydiver and the balance of forces acting on them immediately after they jump.
(b) Explain, in terms of forces, why the skydiver reaches a terminal velocity before opening their parachute.
(c) When the skydiver opens the parachute, their velocity decreases. Explain why this happens and describe the new terminal velocity compared to the previous one.