Question

The potential energy U in Joule of a particle of mass is 4kg moving in the x-y plane is given by the formula U = 6x + 8y + 5. Here x and y are coordinates of the particle in meter. The particle is at (3,5) at t = 0 and v 0 = 0. i and jare the unit vectors across x and y axis respectively. a. Find the force acting on the particle b. Find the kinetic energy of the particle at time t c. Find the time at which it crosses x axis and y axis and Kinetic Energy at that points. d. Find the coordinates of the particle as a function of time t. e. Find the Potential energy of the particle at time t = 3s.

Name: the potential energy u in joule of a particle of mass is 4kg moving in the x y plane is given by the formula u 6x 8y 5 here x and y are coordinates of the particle in meter the particle is at 35 at 2
Uploaded: 2021-11-16T07:56:50-08:00
Duration: 6 min 27 s
Channel: Ameer Said
Description: the potential energy u in joule of a particle of mass is 4kg moving in the x y plane is given by the formula u 6x 8y 5 here x and y are coordinates of the particle in meter the particle is at 35 at 2

          The potential energy U in Joule of a particle of mass is 4kg moving in the x-y plane is given
by the formula U = 6x + 8y + 5. Here x and y are coordinates of the particle in meter.
The particle is at (3,5) at t = 0 and v 0 = 0. i and jare the unit vectors across x and y axis
respectively.
a. Find the force acting on the particle
b. Find the kinetic energy of the particle at time t
c. Find the time at which it crosses x axis and y axis and Kinetic Energy at that points.
d. Find the coordinates of the particle as a function of time t.
e. Find the Potential energy of the particle at time t = 3s.

Added by Max T.

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 4

Instant Answer

Solved by Expert Ameer Said

11/16/2021

Step 1

The potential energy U is given as U = 6x + 8y + 5. Taking the gradient of U, we get ∇U = 6i + 8j. Therefore, the force acting on the particle is F = -6i - 8j. Show more…

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The potential energy U in Joule of a particle of mass is 4kg moving in the x-y plane is given by the formula U = 6x + 8y + 5. Here x and y are coordinates of the particle in meter. The particle is at (3,5) at t = 0 and v 0 = 0. i and jare the unit vectors across x and y axis respectively. a. Find the force acting on the particle b. Find the kinetic energy of the particle at time t c. Find the time at which it crosses x axis and y axis and Kinetic Energy at that points. d. Find the coordinates of the particle as a function of time t. e. Find the Potential energy of the particle at time t = 3s.