Question:
A particle is travelling along a straight line $OX$. The distance $x$ (in metres) of the particle from $O$ at a time $t$ is given by $X=37+27t-t^{3}$ where $t$ is time in seconds. The distance of the particle from $O$ when it comes to rest is
A particle is travelling along a straight line $OX$. The distance $x$ (in metres) of the particle from $O$ at a time $t$ is given by $X=37+27t-t^{3}$ where $t$ is time in seconds. The distance of the particle from $O$ when it comes to rest is
Updated On: Jul 29, 2024
- 81 m
- 91 m
- 101 m
- 111 m
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The Correct Option is B
Solution and Explanation
Given, $x=37 +27 t-t^{3}$
$v=\frac{d x}{d t}=27-3 t^{2}$
According to problem,
$v=0 \Rightarrow 27-3 t^{2}=0$
Here, $t=3 s$
$x=37+27 \times 3-(3)^{2}=91\, m$
$v=\frac{d x}{d t}=27-3 t^{2}$
According to problem,
$v=0 \Rightarrow 27-3 t^{2}=0$
Here, $t=3 s$
$x=37+27 \times 3-(3)^{2}=91\, m$
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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.