A-particle-moves-with-a-speed-of-10-ms-1-from-the-point-2-2-in-the-direction-3i-4j-The-position-vector-after-3-s-is-

Question Number 16656 by Tinkutara last updated on 24/Jun/17

A particle moves with a speed of 10

{ms}^{- 1} from the point (2, - 2) in the

direction 3 \overset{\land}{i} + 4 \overset{\land}{j} . The position vector

after 3 s is

Answered by sma3l2996 last updated on 25/Jun/17

w e h a v e : \overset{\land}{v} = v_{x} \overset{\land}{i} + v_{y} \overset{\land}{j}

a n d u n i t v e c t o r o f 3 i + 4 j i s :

\overset{\land}{e} = \frac{3}{5} \overset{\land}{i} + \frac{4}{5} \overset{\land}{j}

s o : \overset{\land}{v} = 10 . \overset{\land}{e} = 6 \overset{\land}{i} + 8 \overset{\land}{j}

a n d w e h a v e O \overset{\land}{M} = x \overset{\land}{i} + y \overset{\land}{j}

\overset{\land}{v} = \frac{d O \overset{\land}{M}}{d t} \Leftrightarrow \int d O \overset{\land}{M} = \int (6 \overset{\land}{i} + 8 \overset{\land}{j}) d t =

O \overset{\land}{M} (t) = (6 t + c_{x}) \overset{\land}{i} + (8 + c_{y}) \overset{\land}{j}

w h e n t = 0; O \overset{\land}{M} (t = 0) = 2 \overset{\land}{i} - 2 \overset{\land}{j} = c_{x} i + c_{y} j

O \overset{\land}{M} (t) = (6 t + 2) i + (8 t - 2) j

s o w h e n t = 3 s

O \overset{\land}{M} = 20 \overset{\land}{i} + 22 \overset{\land}{j}

s o t h e p o s i t i o n o f p a r t i c l e a f t e r 3 s i s : (20; 22)

Commented by Tinkutara last updated on 25/Jun/17

Thanks Sir!