Classical Mechanics

1D Kinematics

Problem solving with velocity and acceleration - Basic


In a subway station, there are two escalators going upwards toward the exit. One is broken while the other one is working. If a man walks up the broken escalator, it takes 5454 seconds for him to leave the station. If he takes the working escalator while standing still, it takes 2828 seconds for him to leave the station. If this man walks while taking the working escalator, approximately how long will it take for him to leave the station?

Assume that the escalator and man are both move with constant respective velocities.

The length of a clock's second-hand is 45 mm.45\text{ mm}. What is the average velocity of the end point of this second hand during any thirty seconds of time?

An object is positioned at x=0x=0 at time t=0.t=0. It accelerates at a rate of 2.3 m/s22.3\text{ m/s}^2 for 2.62.6 seconds, then it accelerates at a rate of 5.2 m/s2-5.2\text{ m/s}^2 for 2.42.4 seconds. What is the approximate velocity of the object at t=4.4t=4.4 seconds?

Two spaceships initially at rest take off to travel a distance of 2000 km.2000\text{ km}. One spaceship accelerates uniformly at a rate of 40 km/s240 \text{ km/s}^2, and the second one moves with a constant acceleration of 10 km/s2.10 \text{ km/s}^2. How many seconds earlier will the first spaceship reach its destination?

The position of an object moving along the xx-axis with constant acceleration is described as x=72t2+3t+6.x=\frac{7}{2}t^2+3t+6. If tt is in seconds and xx is in meters, what is the acceleration of this object?


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