Question:
An object is projected in x-y plane from the origin at t=0 and its velocity changes according to relation $\bar{v} = a\hat{i}+bx\hat{j}$. Equation of path of particle is
An object is projected in x-y plane from the origin at t=0 and its velocity changes according to relation $\bar{v} = a\hat{i}+bx\hat{j}$. Equation of path of particle is
Updated On: Jul 6, 2022
- Hyperbolic
- Circular
- Elliptical
- Parabolic
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The Correct Option is D
Solution and Explanation
$\frac{dx}{dt} = a, \therefore = at$
$\nu_y = bx = bat$
$\frac{dy}{dt} = bat , \int dy = \int bat \, dt$
$y = \frac{bat^2}{2} $
$y = \frac{bax^2}{2a} = \frac{bx^2}{2a}$
$y \alpha x^2$
i.e. parabolic
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Notes on Motion in a plane
Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration