Question:
A particle moves along Y-axis in such a way that its y-coordinate varies with time $t$ according to the relation $y = 3 +5t + 7t ^2$. The initial velocity and acceleration of the particle are respectively
A particle moves along Y-axis in such a way that its y-coordinate varies with time $t$ according to the relation $y = 3 +5t + 7t ^2$. The initial velocity and acceleration of the particle are respectively
Updated On: Jun 20, 2022
- $14 m$ $s^{-1}, -5m\,s^{-2}$
- $19 m$ $s^{-1}$,$-9\,m$ $s^{-2}$
- $-14\, m$ $s^{-1}$,$-5\,m$ $s^{-2}$
- $5 \,m$ $s^{-1}$,$14\,m$ $s^{-2}$
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The Correct Option is D
Solution and Explanation
Given $y = 3 + 5t+7t^2$
Velocity (v) is defined as rate of change of displacement, also
using $\frac{d}{dx}x^n=nx^{n-1},$ we have
hence $v=\frac{dy}{dt}=5+15t$
Initial velocity at t = 0, is
$v=5ms^{-1}$
Also acceleration a =$\frac{d^2 y}{dt^2}$
$=14 ms^{-2}$
Velocity (v) is defined as rate of change of displacement, also
using $\frac{d}{dx}x^n=nx^{n-1},$ we have
hence $v=\frac{dy}{dt}=5+15t$
Initial velocity at t = 0, is
$v=5ms^{-1}$
Also acceleration a =$\frac{d^2 y}{dt^2}$
$=14 ms^{-2}$
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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.