Question

A particle is moving on a straight-line path with constant acceleration directed along the direction of instantaneous velocity. Which of the following statements are false about the motion of particles?
a) Particle may reverse the direction of motion
b) Distance covered is not equal to magnitude of displacement
c) The magnitude of average velocity is less than average speed
d) All the above.

Answer 1

The particle is moving in a straight line. That means there’s no change in the path of the particle in the entire trip. It is moving with constant acceleration, meaning the particle doesn’t change its acceleration at all. The acceleration direction is in the same direction of instantaneous velocity.

Complete answer:
As the acceleration is constant, the acceleration will not increase or decrease in the entire travel of the particle. The direction of acceleration is in the same direction of instantaneous velocity. Therefore, the particle will not reverse its direction at all. The particle is moving in a straight line which means the distance and displacement is the same for the particle. Also, the particle will not turn in any direction. As it is along a straight path, the distance travelled by the particle will be equal to the displacement of the particle. Also, the direction of the particle is always directed towards the instantaneous velocity of the particle, which tells us that the direction of motion is uniform. Therefore, the average speed is also equal to the average velocity as the distance and displacement is the same.

Therefore, options a, b, c are wrong which says option d is correct.

Additional information:
Average speed is calculated as the ratio between the distance travelled by the particle or object and the time taken by the particle to reach the destination. Average velocity is the ratio between the total displacement of the particle and the total time taken by the particle. The limit of the average velocity as the time elapsed will approach to zero is known as instantaneous velocity. Simply, it is the derivative of distance with respect to time.

Note:
In the above question, the magnitude of average speed and average velocity is the same because the path of the particle is straight and the direction of the motion is in the direction of instantaneous velocity. As the acceleration is constant, there’s no chance the particle will decelerate and come to rest, thus we can confirm that the particle doesn’t change its direction too.