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PhysicsKinematics2-D & 3DEasy2 minPYQ_2020

PhysicsEasysingle choice

A particle starts from the origin of coordinates at time $t = 0$ and moves in the $x - y$ plane with a constant accelerationαin the $y$ -diretion. Its equation of motion is $y = β x^{2}$ . Its velocity component in the $x$ -direction is

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Answer:

Solution:

Equation of motion is $y = β x^{2}$

$\frac{d^{2} y}{{dt}^{2}} = α$

$\frac{d^{2} x}{{dt}^{2}} = 0$

from $y = x$

$\frac{dy}{dt} = 2 x \frac{dx}{dt} β$

$\frac{d^{2} y}{{dt}^{2}} = (2 {(\frac{dx}{dt})}^{2} + 2x \frac{d^{2} x}{{dt}^{2}}) β$

$a_{y} = (2 {(\frac{dx}{dt})}^{2} + 0) β$

$a_{y} = 2 v_{x}^{2} β$

$v_{x} = \sqrt{\frac{a_{y}}{2 β}} = \sqrt{\frac{α}{2 β}}$

Stream:NTA_ABHYASSubject:PhysicsTopic:KinematicsSubtopic:2-D & 3D

⏱ 2mℹ️ Source: PYQ_2020

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