Question:
The motion of a particle is represented by the equation $ S = 8t^3 - 2t^2+ 6t + 7 $ . Find the velocity of the particle at the end of $ 2 $ seconds in $ m s^{-1} $
The motion of a particle is represented by the equation $ S = 8t^3 - 2t^2+ 6t + 7 $ . Find the velocity of the particle at the end of $ 2 $ seconds in $ m s^{-1} $
Updated On: Jun 14, 2022
- $ 108 $
- $ 57 $
- $ 94 $
- $ 41 $
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The Correct Option is C
Solution and Explanation
$S=8t^{3}-2t^{2}+6t+7$
$x=n \frac{\lambda}{t}=8 \left(3t^{2}\right)-2\left(2t\right)+6\left(1\right)+7\left(0\right)$
$=24t^{2}-4t+6$
At $t=2\,s$,
$v=24\left(2\right)^{2}-4\left(2\right)+6$
$=96-8+6$
$=94\,m\,s^{-1}$
$x=n \frac{\lambda}{t}=8 \left(3t^{2}\right)-2\left(2t\right)+6\left(1\right)+7\left(0\right)$
$=24t^{2}-4t+6$
At $t=2\,s$,
$v=24\left(2\right)^{2}-4\left(2\right)+6$
$=96-8+6$
$=94\,m\,s^{-1}$
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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.