Question

If magnitude of average speed and average velocity over a time interval are same, then
(A) The particle must move zero acceleration
(B) The particles must move with non-zero acceleration
(C) The particles must be at rest
(D) The particles must move in a straight line without turning back

Answer 1

Hint: The particle gains speed as well as velocity when it moves from its stationary position. The magnitude of speed and velocity during the time of traveling gives information about the motion of the particle and in which direction this motion of the particle occurs.

Complete step by step answer:
Generally, when a body or particle moves from one place to another place, we can observe that its speed and velocity varies with time. But if the particle acquires uniform motion and travels in the straight direction, it can achieve constant speed and constant velocity.
Speed gives information about how fast a particle travels or covering the distance in its journey with time. For the constant average speed, the particles must cover the same amount of distance in every small interval. Whereas the particles' velocity gives information about the changes occurring in the speed with the time and in which direction the motion of the particles occurs. When the particle's acceleration is zero, the particles that move in a straight line cover the same distance as the displacement in the same interval of time. So, due to this reason, the magnitude of the average speed and average velocity over a time interval will become the same.
Therefore, if magnitudes of average speed and average velocity over a time interval are same, then the particles must move in a straight line without turning back

So, the correct answer is “Option D”.

Note:
Remember that the particle speed is related to distance and particle velocity is related to the displacement that’s why their same value gives the same amount of distance and displacement. For achieving this condition, the particles move in a straight line.