運動與運動學圖像：練習題

A bicycle and rider have a total mass of \( 80 \text{ kg} \) and move at a constant velocity of \( 4.5 \text{ m s}^{-1} \).
What is the magnitude of the momentum of the bicycle and rider?

A car accelerates uniformly from rest at \(2.5 \text{ m s}^{-2}\) for a distance of \(50 \text{ m}\).
What is the final velocity of the car?

A block of mass \( 0.40 \text{ kg} \) moving at \( 5.0 \text{ m s}^{-1} \) collides with a stationary block of mass \( 0.60 \text{ kg} \) on a frictionless horizontal surface. The two blocks stick together and move with a common velocity.
What is the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision?

A bowling ball of mass \( 7.0 \text{ kg} \) rolls down a lane at \( 6.0 \text{ m s}^{-1} \).
What is the magnitude of the momentum of the bowling ball?

An electric motor is used to lift a load of mass \( 120 \text{ kg} \) through a vertical height of \( 15.0 \text{ m} \) in a time of \( 25.0 \text{ s} \). The efficiency of the motor system is \( 70.0\% \).
What is the electrical power input to the motor? (Take \( g = 9.81 \text{ m s}^{-2} \))

A car of mass \( 1200 \text{ kg} \) accelerates from rest to a velocity of \( 20 \text{ m s}^{-1} \) in a time of \( 8.0 \text{ s} \).
Calculate the average power developed by the engine during this acceleration.

A ball is kicked from the ground with an initial velocity of \( 15 \text{ m s}^{-1} \) at an angle of \( 40^{\circ} \) to the horizontal.
Calculate the horizontal distance the ball travels before returning to the ground.
(Take \( g = 9.81 \text{ m s}^{-2} \))

A ball is thrown from the top of a building with an initial velocity of \( 12 \text{ m s}^{-1} \) at an angle of \( 30^{\circ} \) above the horizontal. If the ball hits the ground \( 3.5 \text{ s} \) after it was thrown, determine the height of the building.
(Take \( g = 9.81 \text{ m s}^{-2} \) and ignore air resistance.)

The diagram shows a projectile launched from horizontal ground with an initial velocity of \( 22 \text{ m s}^{-1} \) at an angle of \( 40^{\circ} \) to the horizontal. Air resistance is negligible.

(a) Calculate the time taken for the projectile to reach its maximum height.
(b) Calculate the maximum height reached by the projectile above the ground.
(c) Calculate the horizontal distance (range) travelled by the projectile when it returns to the ground level.

A small motor is used to lift a load of mass 0.50 kg through a vertical height of 2.0 m. The motor is connected to a 12 V power supply and draws a constant current of 1.5 A. The time taken for the lift is 6.5 s.

(a) Calculate the useful work done by the motor in lifting the load.
(b) Calculate the total electrical energy input to the motor during this time.
(c) Determine the efficiency of the motor system.
(d) After reaching the height of 2.0 m, the load is released from rest. Calculate its velocity just before it hits the ground, assuming air resistance is negligible.
(Take \( g = 9.81 \text{ m s}^{-2} \))