Question

Displacement of a body is given by $x=1+3t+3{{t}^{2}}$. The value of instantaneous acceleration is given by?
(A) 4 units
(B) 6 units
(C) 5 units
(D) 2 units

Answer 1

Hint:We know that when we differentiate the displacement of a body twice, we get the acceleration of the body at that time. Hence we can apply the same in the given question by differentiating the given value of displacement with respect to time.

Complete step by step answer:
In the question, we are given that the displacement of the body is
$x=1+3t+3{{t}^{2}}$
In order to obtain velocity of the body, we differentiate the given displacement with respect to time
That is $v=\dfrac{dx}{dt}=\dfrac{d}{dt}(1+3t+3{{t}^{2}})=3+4t$
In order to obtain the acceleration of the body, we further differentiate the velocity with respect to time,
That is $a=\dfrac{dv}{dt}=4$
Hence, upon differentiation, we have obtained the value of acceleration of the body, that is 4 units.
Therefore we can conclude that option A is the correct answer among the four.

Note:If the acceleration is given as an equation varying with time, we can integrate the acceleration twice to get the displacement of the body.Also, if we differentiate acceleration once more we get jerk or jolt. Jerk or jolt is the rate at which the acceleration of any object changes according to time. As it possesses both magnitude and direction, it is a vector quantity. Jerk is expressed in m/s3 (SI units) or standard gravities per second (g/s). Further differentiation of jerk gives jounce, which is the rate of change of jerk.