Physics

Problem

A particle moving along the

x

-axis has an initial velocity of

2\,\text{m s}^{-1}

t=0

. It experiences a constant acceleration of

+3\,\text{m s}^{-2}

for the next

4\,\text{s}

. Immediately after that, a constant acceleration of

-4\,\text{m s}^{-2}

acts on the particle until its velocity becomes zero. Answer the following: (i) Calculate the velocity of the particle at the instant

t=4\,\text{s}

. (ii) Determine the additional time taken (after

t=4\,\text{s}

) for the particle to come to rest. (iii) Compute the total displacement of the particle from

t=0

until it stops. (iv) What is the greatest speed attained by the particle during this entire motion? a. (i) Velocity at

t=4\,\text{s}

. b. (ii) Additional time required to come to rest. c. (iii) Total displacement from start to rest. d. (iv) Greatest speed attained in the motion.

Intuitive explanation

This problem traces a particle through two distinct phases of motion, each with different constant accelerations. The key is to treat each phase separately using kinematic equations, then connect them: the final velocity of phase one becomes the initial velocity of phase two. You'll need to track how velocity changes linearly with time under each acceleration, and use the relationship between velocity, acceleration, and displacement to find the total distance traveled.

Intuitive explanation

Browse the problem library