Question

the initial and final position vector of a particle is given by r1= i+j+k and r2 2i+2j+2k and time taken for the displacement is 10,find the average velocity

Answer 1

Answer:

$\tt{0.1 \hat{i} + 0.1 \hat{j} + 0.1 \hat{k}}$ distance unit/sec

Given :

$\tt \rightarrow r_{1} = \hat{i} + \hat{j} + \hat{k} \: \\ \\ \tt \rightarrow r_{2} = 2 \hat{ i} + 2 \hat{j} + 2 \hat{k} \: \\ \\ \tt \rightarrow t = 10 \: sec$

Solution :

The total displacement is the particle covers is given by :

$\tt{\Delta \: r = r_2 - r_1}$

Here , while substraction , we can directly substract the individual coordinates to get the coordinates of the resultant .

$\tt = (2 \hat{i} + 2 \hat{j} + 2 \hat{k}) - ( \hat{i} + \hat{j} + \hat{k}) \\ \\ \tt = (2 - 1) \hat{i} + (2 - 1) \hat{j} + (2 - 1) \hat{k} \\ \\ \tt = \hat{i} + \hat{j} + \hat{k}$

The formula of velocity is given by :

$\boxed{ \boxed{\tt{ \red{velocity} = \dfrac{ \purple{displacement}}{\orange{time}} }}}$

$\tt v = \dfrac{ \hat{i} + \hat{j} + \hat{k}}{10}$

$\underline{ \sf v =( 0.1 \hat{i} + 0.1 \hat{j} + 0.1 \hat{k} \: ) distance \: unit {sec}^{ - 1} }$