A.1 Kinematics：練習問題

Which of the following quantities is a vector?

A car travels a total distance \(d\). It covers the first one-third of the distance at a constant speed \(v_1\) and the remaining two-thirds of the distance at a constant speed \(v_2\). What is the average speed of the car for the entire journey?

A stone is dropped from rest into a deep well. The sound of the splash is heard at the top of the well after a total time \(T\). If the depth of the well is \(d\), the speed of sound is \(v_s\), and acceleration due to gravity is \(g\), which expression correctly represents \(T\)?

An object is moving with a constant negative acceleration. Which of the following statements must be true regarding its velocity?

A car starts from rest and accelerates at a constant rate \(a\) for a time interval \(t\). It then immediately decelerates at a constant rate \(2a\) until it comes to a complete stop. What is the total distance traveled by the car during the entire motion?

A person walks \(4.0\text{ km}\) in \(1.0\text{ hour}\) and then remains stationary for another \(1.0\text{ hour}\). Calculate the average speed for the entire \(2.0\text{ hour}\) journey.

An object starts from rest and moves with a constant acceleration. If the distance traveled during the first time interval Δt is \(d_1\), determine the distance \(d_2\) traveled during the second identical time interval Δt in terms of \(d_1\).

For a projectile launched from level ground at an angle \(θ\) to the horizontal, the horizontal range is found to be exactly three times the maximum height reached. Calculate the value of \(θ\).

A research vessel uses a sonar pulse to determine the depth of a seabed. The speed of sound in seawater is \(1530\text{ m s}^{-1}\). A pulse is emitted and the reflection is detected \(0.40\text{ s}\) later.
(a) Define average speed.
(b) Calculate the total distance traveled by the sound pulse.
(c) Determine the depth of the seabed at this location.
(d) State one factor that might affect the speed of sound in seawater, thereby influencing the accuracy of this measurement.

A ball is projected vertically upwards from the roof of a building that is 25.0 m high. The initial speed of the ball is 12.0 m s^-1. Air resistance is negligible. (Use \(g = 9.81\text{ m s}^{-2}\))

(a) Calculate the time taken for the ball to reach its maximum height above the roof.
(b) Determine the total distance traveled by the ball from the moment it is released until it strikes the ground at the base of the building.
(c) Calculate the magnitude of the velocity of the ball at the moment it hits the ground.