Question

2. If a body lanels for time 't with speed vi and
then it further travels for time t with speed v2
find the average speed.​

Answer 1

Answer:

Given:

Body travels with v1 for time t and again with v2 for time t.

To find:

Average velocity in whole journey

Concept:

Average speed is always calculated as the ratio of total distance travelled to the total time taken.

For average Velocity, we take the ratio of total displacement to the total time taken.

Calculation:

$\boxed{ \sf{ \bold{ \red{avg. \: v = \dfrac{total \: distance}{total \: time}}}}}$

$= > avg. \: v = \dfrac{(v1 \times t) + (v2 \times t)}{(t + t)}$

$= > avg. \: v = \dfrac{(v1 + v2)t}{2t}$

$= > avg. \: v = \dfrac{v1 + v2}{2}$

So we can very well understand that the average speed is the arithmetic mean of the speed data available in this case.

So final answer :

$\boxed{ \sf{ \red{ \bold{ avg. \: v = \dfrac{v1 + v2}{2}}}}}$

Answer 2

Answer:

$\underline{ \boxed{ \bold{ \huge{ \purple{Answer}}}}} \\ \\ \star \sf \: \bold{ \blue{Given}} \\ \\ \implies \sf \: initial \: velocity = V{ \tiny{1}} \\ \\ \implies \sf \: final \: velocity = V{ \tiny{2}} \\ \\ \implies \sf \: initial \: time = t{ \tiny{1}} \\ \\ \implies \sf \: final \: time = t{ \tiny{2}} \\ \\ \implies \sf \: t{ \tiny{1}} = t{ \tiny{2}} = t \\ \\ \star \sf \: \bold{ \blue{To \: Find}} \\ \\ \implies \sf \: average \: velocity \\ \\ \star \sf \: \bold{ \blue{Formula}} \\ \\ \implies \sf \: \underline{ \boxed{ \bold{ \pink{V{ \tiny{av}} = \frac{d{ \tiny{1}} + d{ \tiny{2}}}{t{ \tiny{1}} + t{ \tiny{2}}} }}}} \\ \\ \star \sf \: \bold{ \blue{Calculation}} \\ \\ \mapsto \sf \: V{ \tiny{av}} = \frac{V{ \tiny{1}}t \: + V{ \tiny{2}}t}{t + t} = \frac{t(V{ \tiny{1}} + V{ \tiny{2}})}{2t} \\ \\ \mapsto \sf \: \underline{ \boxed{ \bold{ \red{V{ \tiny{av}} = \frac{V{ \tiny{1}} +V{ \tiny{2}} }{2} }}}} \: \: \orange{ \star}$