Question:
If the velocity of a particle is given by $ v=(180-16x)^{1/2}\,m/s$ . then its acceleration will be
If the velocity of a particle is given by $ v=(180-16x)^{1/2}\,m/s$ . then its acceleration will be
Updated On: Jun 8, 2024
- zero
- $ 8\,m/s^{2}$
- $ -8\,m/s^{2}$
- $ 4\,m/s^{2}$
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The Correct Option is C
Solution and Explanation
$a=\frac{d v}{d t}=\frac{d x}{d t} \frac{d v}{d x}=v \frac{d v}{d x}$
$v=(180-16 x)^{\frac{1}{2}}$
$v^{2}=180-16 x$
Diff. both sides wrt. $x$,we get:
$2 v \frac{d v}{d x}=-16$
$v \frac{d v}{d x}=a=-8\, m / s ^{2}$
$v=(180-16 x)^{\frac{1}{2}}$
$v^{2}=180-16 x$
Diff. both sides wrt. $x$,we get:
$2 v \frac{d v}{d x}=-16$
$v \frac{d v}{d x}=a=-8\, m / s ^{2}$
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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.