Question:
The displacement of a particle is given by $x = a_0 + \frac{a_1 t}{2} - \frac{a_2 t^2}{3}$, what is its acceletion ?
The displacement of a particle is given by $x = a_0 + \frac{a_1 t}{2} - \frac{a_2 t^2}{3}$, what is its acceletion ?
Updated On: Jun 7, 2022
- $\frac{2a_2}{3}$
- $- \frac{2a_2}{3}$
- $a_2$
- zero
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The Correct Option is B
Solution and Explanation
Given, $x = a_0 + \frac{a_1 t}{2} - \frac{a_2 t^2}{3}$
Differentiating with respect to $t$, we get
$\frac{dx}{dt} =v = \frac{a_1}{2} - \frac{2a_2 t}{3}$
Again differentiating with respect to $t$, we get
$\frac{d^2 x}{dt^2}= a = -\frac{2a_2}{3}$
$\Rightarrow $ acceleration, $a = -\frac{2a_2}{3}$
Differentiating with respect to $t$, we get
$\frac{dx}{dt} =v = \frac{a_1}{2} - \frac{2a_2 t}{3}$
Again differentiating with respect to $t$, we get
$\frac{d^2 x}{dt^2}= a = -\frac{2a_2}{3}$
$\Rightarrow $ acceleration, $a = -\frac{2a_2}{3}$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.