Question

When an object undergoes acceleration then which one of the following is true?
${\text{A}}{\text{.}}$ Its speed always increases
${\text{B}}{\text{.}}$ Magnitude of velocity may remain constant
${\text{C}}{\text{.}}$ It always falls towards the earth
${\text{D}}{\text{.}}$ A force always acts on it

Answer 1

- Hint- Here, we will proceed by defining the terms velocity and acceleration in reference to kinematics. Then, we will write down the general mathematical formula for acceleration and then, we will discuss each one of the options given in the problem.

Complete step-by-step solution -

Velocity is the rate that an object moves from one place to another. Velocity is a vector quantity, which means it has both a magnitude, called speed, and a direction.
Acceleration, also a vector quantity, is the rate at which an object changes its velocity.
Mathematically, acceleration (average) can be expressed as
Acceleration (average) = \[\dfrac{{{\text{Change in velocity}}}}{{{\text{Change in time}}}} = \dfrac{{\overrightarrow {{v_2}} - \overrightarrow {{v_1}} }}{{{t_2} - {t_1}}}\]
where \[\overrightarrow {{v_2}} \] is the final velocity vector corresponding to time \[{t_2}\] and \[\overrightarrow {{v_1}} \] is the initial velocity corresponding to time \[{t_1}\].
Now we will observe each option carefully with the condition given in the problem, to check which one is correct.
When an object undergoes acceleration then, its speed can increase or decrease or remain constant. When the speed is decreasing, we call it deceleration. There can be a case where only the direction of the velocity is changing and its magnitude (i.e., speed) remains constant. So, when an object undergoes acceleration then it is not necessary that its speed will always be increasing. So, option A is incorrect.
When an object undergoes acceleration then the magnitude of velocity (i.e., its speed) may increase or may decrease or may remain constant. Hence, option B is correct.
When an object undergoes acceleration then it is not always necessary that the object is always falling towards the earth. Objects falling towards the earth is one example of acceleration because a gravitational force is experienced by the object (due to its mass) when it falls towards the earth. So, option C is incorrect.
It is not necessary that when an object undergoes acceleration then a force will always act on it. So, option D is incorrect.

Note- In contrast, instantaneous acceleration is measured over a short time interval. Instantaneous acceleration is then the limit of average acceleration as the time interval approaches zero or alternatively, acceleration is the derivative of velocity. The mathematical expression for instantaneous acceleration is $\mathop {\lim }\limits_{\Delta t \to 0} \dfrac{{\Delta v}}{{\Delta t}} = \dfrac{{dv}}{{dt}}$.