Λparticle moving in x-y plane is at origin at time t=0 ....

\Lambda particle moving in $x-y$ plane is at origin at time $t=0 .$ Velocity of the particle is $(2 \vec{i}-4 \hat{j}) \mathrm{m} / \mathrm{s}$ and acceleration $i s(4 \hat{i} \mid \hat{j}) \mathrm{m} / \mathrm{s}^{2}$. Find at $t=2 \mathrm{~s}$ (a) velocity of particle and (b) coordinates of particle.

\Lambda particle moving in $x-y$ plane is at origin at time $t=0 .$ Velocity of the particle is $(2 \vec{i}-4 \hat{j}) \mathrm{m} / \mathrm{s}$ and acceleration $i s(4 \hat{i} \mid \hat{j}) \mathrm{m} / \mathrm{s}^{2}$. Find at $t=2 \mathrm{~s}$
(a) velocity of particle and
(b) coordinates of particle.

Key Concepts

Vector Operations and Component Addition

Basic vector operations, such as addition and scalar multiplication, are applied on a component-by-component basis to calculate resultant vectors. This is fundamental in problems involving motion, as it allows combining separate contributions (like initial velocity and acceleration effects) to yield the net velocity or displacement.

Equations of Motion under Constant Acceleration

These equations describe how the velocity and position of an object change over time when acceleration is constant. They include formulas like v = v0 + at and r = r0 + v0t + (1/2)at^2, which are essential for predicting future states of moving particles based on initial conditions and constant acceleration.

Two-Dimensional Kinematics

This concept involves analyzing motion in the plane by breaking vectors into their x and y components. It allows for the separate treatment of each component when calculating velocities and displacements, making complex motion easier to study and understand via component-wise analysis.

Transcript

00:01 Hello everyone.

00:02 Let's solve the following question.

00:03 In this question we are given a particle in xy plane.

00:10 The particle starts to moving at time t is equal to zero from the reason and the velocity initial velocity v of the particle, let us say it is u.

00:21 Initial velocity u vector of the particle is 2 i cap minus 4 j cap meter per second and the initial acceleration.

00:31 A vector of the particle is given 4 i cap plus j cap meter per second.

00:39 We have to find at time at time t is equal to 2 second the velocity of the particle, velocity of particle and second thing we have to find the coordinates of particle.

00:59 The second thing that we have to find is coordinates of particle.

01:06 Now first of all, we can write the initial velocity into its components form, which will give us u -vector is equal to ux i -caf plus u .s.

01:17 J -cap equals to 2 i -cap minus 4 j -caf meter per second.

01:22 It means ux is equal to 2 and u y is equals to minus 4.

01:29 Similarly for the acceleration a vector we can write a x i cap plus a y j cap so this will be equals to 4 i cap plus j cap which means a x will be equals to 4 and a y will be equals to 1.

01:47 Now we can find out the velocity and the coordinates of the particle.

01:52 Of all for the velocity, v, we can write vx equals to ux plus a, t and vy is equals to uy plus ay into t.

02:07 Ux is 2 plus ax...

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