Velocity and Acceleration — Prelims Questions

A particle moves along the x-axis such that its position is given by \( x(t) = 2t^3 - 9t^2 + 12t + 5 \) meters, where \( t \) is in seconds. What is the acceleration of the particle when its velocity is zero?

A particle starts from rest and moves with constant acceleration \( a \). Its velocity after time \( t \) is \( v \). What is the average velocity of the particle during this time interval?

The velocity-time graph for a particle moving along a straight line is shown. What is the displacement of the particle from \( t = 0 \) to \( t = 4 \text{ s} \)? (Assume a graph where velocity increases linearly from 0 to 10 m/s in 2s, then stays constant at 10 m/s for 2s).

Which of the following statements is true about an object moving with constant velocity?

A particle's velocity is given by \( v(t) = (3t^2 - 6t) \text{ m/s} \). Find the average acceleration of the particle between \( t = 1 \text{ s} \) and \( t = 3 \text{ s} \).

A ball is thrown vertically upwards. Which of the following statements correctly describes its velocity and acceleration at the highest point of its trajectory?