Question

The acceleration of a particle changes when
A. Direction of velocity changes
B. Magnitude of velocity changes
C. Either of above
D. Speed is constant

Answer 1

The definition and the concept behind acceleration and reason behind acceleration of an object needs to be looked upon in order to determine the correct option.The relation between acceleration and velocity is determined and whether velocity is a vector or a scalar quantity needs to be found out.

Complete answer:
The above problem revolves around the concept of acceleration and its cause, that is, when acceleration of a body occurs. In order to find the correct option we first need to define acceleration and the concept behind it.Acceleration is basically a measure of how fast or slow a body is moving. The term acceleration comes into picture only when a body is moving with a certain velocity. Hence, it is directly related to the velocity of the body in motion.

By definition, acceleration is said to be the rate of change of velocity with time. This means that the velocity of the body should be constantly changing or varying with respect to time. When the velocity changes at every instant of time then it is said to be constantly varying with time and hence this is when acceleration is introduced.

Mathematically acceleration is given as:
$a = \dfrac{{dv}}{{dt}}$
This means that acceleration is equivalent to the rate of change of velocity differentiated with respect to time. Since, we can see that this is how acceleration is directly related to velocity we can say that when there is velocity variation then the acceleration of the particle also undergoes a change.

Now, we come to the quantity known as velocity. The velocity of a body is known to be a vector quantity which means that it consists of both magnitude as well as direction. The direction in which the body is moving towards is also considered in the case of vector quantities. This magnitude is the value of the velocity, that is, at what velocity the body is travelling in.

Since, velocity depends on both magnitude as well as direction and since acceleration occurs with a constant change in velocity we can say that when either the direction of velocity changes or when the magnitude of velocity changes with time then acceleration takes place.The last option is incorrect because the quantity that introduces acceleration is the velocity and not speed as speed is a scalar quantity. Therefore, when either of the options A or B occurs then acceleration of a particle changes.

Thus the correct option is option C.

Note: When the body is said to be at rest or stationary then the velocity of the body is zero which makes the acceleration of the body to become zero as well. Another instance when acceleration is zero is when the velocity of the body with time is constant and does not show any variation. The acceleration of a body can be negative also and this is known as deceleration.