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JEE Main 20244 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Morning Shift
Subject
Physics
Chapter
Motion in Two Dimensions

JEE Main 2024 · 4 April · Morning Shift · Physics · Motion in Two Dimensions

The co-ordinates of a particle moving in x-y plane are given by :...

The co-ordinates of a particle moving in x−yx-y plane are given by : x=2+4t,y=3t+8t2x=2+4 \mathrm{t}, y=3 \mathrm{t}+8 \mathrm{t}^2. The motion of the particle is :

Options

  1. Auniformly accelerated having motion along a parabolic path.
  2. Buniform motion along a straight line.
  3. Cuniformly accelerated having motion along a straight line.
  4. Dnon-uniformly accelerated.

Correct answer

A. uniformly accelerated having motion along a parabolic path.

Step-by-step solution

x=2+4tdxdt=vx=4dvxdt=ax=0y=3t+8t2dydt=vy=3+16tdvydt=ay=16\begin{aligned} & x=2+4 t \\ & \frac{d x}{d t}=v_x=4 \\ & \frac{d v_x}{d t}=a_x=0 \\ & y=3 t+8 t^2 \\ & \frac{d y}{d t}=v_y=3+16 t \\ & \frac{d v_y}{d t}=a_y=16 \end{aligned} the motion will be uniformly accelerated motion. For path x=2+4t(x−2)4=t\begin{aligned} & \mathrm{x}=2+4 \mathrm{t} \\ & \frac{(\mathrm{x}-2)}{4}=\mathrm{t} \end{aligned}
Put this value of tt is equation of yy y=3y=3\left(\frac{x-2}{4}\right)+8(x−24)2\left(\frac{x-2}{4}\right)^2 this is a quadratic equation so path will be parabola.
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