Question

Statement- $1$ : A positive acceleration can be associated with a 'slowing down' of the body.
Statement- $2$ : The origin and the positive direction of an axis are a matter of choice.
(A) Statement- $1$ is false, Statement- $2$ is true.
(B) Statement- $1$ is true, Statement- $2$ is true; Statement- $2$ is a correct explanation for Statement- $1$ .
(C) Statement- $1$ is true, Statement- $2$ is true; Statement- $2$ is not a correct explanation for Statement- $1$ .
(D) Statement- $1$ is true, Statement- $2$ is false.

Answer 1

Hint: Acceleration is described as the rate of change in speed relative to time. Acceleration, since it has both magnitude and direction, is a vector quantity. It is also the second derivative of position with respect to time, or it is the first derivative of velocity with respect to time.

Formula Used: We can define acceleration by the following way:
Acceleration $={\displaystyle \frac{\text{final velocity}-\text{initial velocity}}{\text{time}}}$
Or we can say
 $a={\displaystyle \frac{v_f-v_i}{t}}$
 $a$ is the acceleration in $\text{m}/{\text{s}}^2$
 ${\text{v}}_{\text{f}}$ is the final velocity in $\text{m}/s$
 ${\text{v}}_{\text{i}}$ is the initial velocity in $m/s$
 $t$ is the time interval in seconds.

Complete Step-by-Step Solution
Let us consider the first statement. In this case, let us suppose that a body has a positive acceleration in a particular direction. And now let us assume that the body has velocity in the direction opposite to it. So, in this case the velocity of the body can slow down. So, we can say that it is not necessary that a body should possess negative velocity for it to slow down. The body will slow down if the direction of acceleration is opposite to the direction of motion.
So, we can say that if a body has positive velocity, then we need to apply negative acceleration to slow down the body.
Similarly, if a body has negative velocity, then we need to apply positive acceleration to slow down the body.
So, we can take positive or negative velocity as per our requirements. Like if we want negative acceleration, then we have to choose positive velocity and if we want positive acceleration, then we have to choose positive acceleration. It is a matter of choice which we have to decide. So, the second statement is also true. And it is an explanation of the first statement.
Hence, statement $1$ is true and statement $2$ is also true and the second statement is the correct explanation of statement $1$ .
So, the correct option is (B.)

Note
Acceleration is defined as the change in an object's velocity in relation to time. Velocity is defined as an object's speed in a specific direction. This question can easily be solved if we use the concept of both these terms.