Question

a body lying initially at point(3,7) starts moving with a constant acceleration of 4i.its position after 3 second is

Answer 1

This is the answer of your question.

Answer 2

a body lying initially at point (3, 7) starts moving with a constant acceleration of 4i m/s².

intial position of body , $\vec{r}=(3\hat{i}+7\hat{j})\:m/s$
so, component of position of body in x - direction is $r_x=3$
component of position of body in y - direction is $r_y=7$
acceleration, $\vec{a}=4\hat{i}\:m/s^2$

use formula, $S=S_0+ut+\frac{1}{2}at^2$
here , a is acceleration, t is time taken and So is initial position of particle.

in x - direction,
S = X , $S_0=r_x=3$
$a_x=a=4$ and t = 3

so, X = 3 + 0.3 + 1/2 × 4 × 3² = 3 + 18 = 21
X = 21 .......(1)

in Y - direction,
S = Y, $S_0=r_y$, t = 3sec
$a_y=0$

Y = 7 + 0.3 + 1/2 × 0 × 3² = 7
Y = 7........(2)

now, position of particle after 3 second.
$\vec{S}=X\hat{i}+Y\hat{j}$

$\vec{S}=21\hat{i}+7\hat{j}$.