The position vector of a particle is given by | vedclass

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

Question

(A) The position vector is given by $\vec{r}(t) = 3t^2 \hat{i} + 4t^2 \hat{j} + 7 \hat{k}$.At $t = 0 \, s$,the initial position is $\vec{r}_1 = 3(0)^2

Vedclass · Accepted Answer

$500$

Vedclass · Answer

(A) The position vector is given by $\vec{r}(t) = 3t^2 \hat{i} + 4t^2 \hat{j} + 7 \hat{k}$.At $t = 0 \, s$,the initial position is $\vec{r}_1 = 3(0)^2 \hat{i} + 4(0)^2 \hat{j} + 7 \hat{k} = 7 \hat{k}$.At $t = 10 \, s$,the final position is $\vec{r}_2 = 3(10)^2 \hat{i} + 4(10)^2 \hat{j} + 7 \hat{k} = 300 \hat{i} + 400 \hat{j} + 7 \hat{k}$.The displacement vector is $\Delta \vec{r} = \vec{r}_2 - \vec{r}_1 = (300 \hat{i} + 400 \hat{j} + 7 \hat{k}) - (7 \hat{k}) = 300 \hat{i} + 400 \hat{j}$.Since the particle moves in a straight line (the ratio of components $x$ and $y$ is constant),the distance traversed is equal to the magnitude of the displacement.Distance $= |\Delta \vec{r}| = \sqrt{(300)^2 + (400)^2} = \sqrt{90000 + 160000} = \sqrt{250000} = 500 \, m$.

The position vector of a particle is given by the expression $\vec{r} = 3t^2 \hat{i} + 4t^2 \hat{j} + 7 \hat{k}$. The distance traversed in the first $10 \, s$ is ......... $m$.

Similar Questions

What is mechanics? Give definitions of its sub-branches.

When is an object said to be in motion? What is meant by the description of an object's motion?

$A$ cyclist starts from the point $P$ of a circular ground of radius $2 \,km$ and travels along its circumference to the point $S$. The displacement of a cyclist is:

The position vector of a moving particle at time $t$ is $r = 3 \hat{i} + 4t \hat{j} - t \hat{k}$. Its displacement during the time interval $t = 1 \ s$ to $t = 3 \ s$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module