A particle moves from the point (2.0hat i + 4 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given:Initial position $\vec{r}_0 = (2.0\hat i + 4.0\hat j) \, m$Initial velocity $\vec{u} = (5.0\hat i + 4.0\hat j) \, m/s$Acceleration $\vec{a}

Vedclass · Accepted Answer

$20\sqrt{2} \, m$

Vedclass · Answer

(B) Given:Initial position $\vec{r}_0 = (2.0\hat i + 4.0\hat j) \, m$Initial velocity $\vec{u} = (5.0\hat i + 4.0\hat j) \, m/s$Acceleration $\vec{a} = (4.0\hat i + 4.0\hat j) \, m/s^2$Time $t = 2 \, s$Using the equation of motion $\vec{r}(t) = \vec{r}_0 + \vec{u}t + \frac{1}{2}\vec{a}t^2$:$\vec{r}(2) = (2.0\hat i + 4.0\hat j) + (5.0\hat i + 4.0\hat j)(2) + \frac{1}{2}(4.0\hat i + 4.0\hat j)(2)^2$$\vec{r}(2) = (2.0\hat i + 4.0\hat j) + (10.0\hat i + 8.0\hat j) + \frac{1}{2}(4.0\hat i + 4.0\hat j)(4)$$\vec{r}(2) = (2.0\hat i + 4.0\hat j) + (10.0\hat i + 8.0\hat j) + (8.0\hat i + 8.0\hat j)$$\vec{r}(2) = (2.0 + 10.0 + 8.0)\hat i + (4.0 + 8.0 + 8.0)\hat j$$\vec{r}(2) = (20.0\hat i + 20.0\hat j) \, m$The distance from the origin is the magnitude of the position vector:$|\vec{r}(2)| = \sqrt{20^2 + 20^2} = \sqrt{400 + 400} = \sqrt{800} = 20\sqrt{2} \, m$.

Similar Questions

$A$ particle of mass $m$ is moving in the $xy$-plane such that its velocity at a point $(x, y)$ is given as $\vec{v} = \alpha(y \hat{i} + 2x \hat{j})$,where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ acting on the particle?

$A$ scooter going due east at $10\, ms^{-1}$ turns right through an angle of $90^\circ$. If the speed of the scooter remains unchanged in taking the turn,the change in the velocity of the scooter is

At any time $t$,the coordinates of a moving particle are $x = at^2$ and $y = bt^2$. The speed of the particle is

$A$ particle moves along a circle of radius $R$ with kinetic energy $K = as^2$,where $s$ is the distance traveled. What is the net force acting on the particle?

Vedclass Test Series

Exam Paper Generator

Online Exam Module