Motion in a Straight Line — Prelims Questions

A car travels from point A to point B at a constant speed of $40,\text{km/h}$ and returns from B to A at a constant speed of $60,\text{km/h}$. What is the average speed for the entire journey?

A particle starts from rest and moves with constant acceleration. The ratio of displacement in the $n^{\text{th}}$ second to the displacement in the $(n+1)^{\text{th}}$ second is:

A ball is thrown vertically upwards with an initial velocity of $20,\text{m/s}$ from the top of a $25,\text{m}$ high building. Taking $g = 10,\text{m/s}^2$, what is the total time taken for the ball to reach the ground?

The position-time graph for an object moving along a straight line is shown below. Which of the following statements is true about the motion?

Two cars, A and B, are moving in the same direction. Car A is moving at $10,\text{m/s}$ and car B at $15,\text{m/s}$. If car B is $100,\text{m}$ ahead of car A, how long will it take for car A to catch up with car B?

An object moves along the x-axis. Its position is given by $x(t) = 3t^2 - 2t + 1$, where $x$ is in meters and $t$ is in seconds. What is the instantaneous velocity of the object at $t = 2,\text{s}$?

A body is dropped from a height $H$. If it covers a distance $H/2$ in the last second of its motion, what is the total time of fall? (Take $g = 10,\text{m/s}^2$)