A particle starts moving such that position with respect to origin O varies with time t as x{t} = 2t m. Find
(a) average velocity between (i) t = 0 & t = 1s (ii) t = 0 & t = 2s (iii) t = 1s & t = 2s
(b) instantaneous velocity at general time t.

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Solution

Average velocity $= \frac{Change in position}{time interval}$
position at $t = 0$ , $x (0) = 0 m e t e r$
at $t = 1 s$ , $x (1) = 2 m e t e r$
at $t = 2 s e c o n d$ , $x (2) = 4 m e t e r$

(1). Average velocity = $(1 - 0) / (1 - 0) = 1 m / s$
(2) Average velocity $= (4 - 0) / (2 - 0) = 2 m / s$
(3) Average velocity $= (4 - 2) / (2 - 1) = 2 m / s$
(b) Instantaneous velocity= $\frac{d x}{d t} = 2 m / s$

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A particle starts moving such that position with respect to origin O varies with time t as x{t} = 2t m. Find(a) average velocity between (i) t = 0 & t = 1s (ii) t = 0 & t = 2s (iii) t = 1s & t = 2s(b) instantaneous velocity at general time t.

Average velocity=Change in positiontime intervalposition at t=0, x(0)=0meterat t=1s,x(1)=2meterat t=2second,x(2)=4meter(1). Average velocity =(1−0)/(1−0)=1m/s(2) Average velocity=(4−0)/(2−0)=2m/s (3) Average velocity =(4−2)/(2−1)=2m/s(b) Instantaneous velocity=dxdt=2m/s

A particle starts moving such that position with respect to origin O varies with time t as x{t} = 2t m. Find
(a) average velocity between (i) t = 0 & t = 1s (ii) t = 0 & t = 2s (iii) t = 1s & t = 2s
(b) instantaneous velocity at general time t.