Question

a particle transversed along a straight line for first half time with velocity V0 for the remaining part half of the distance is transversed with velocity V1 and other half of the distance with V2 find the mean velocity of particle for total journey.​

Answer 1

Here is Your Answer

Answer :-

Distance =x+x=2x

Distance =x+x=2xTime taken =x/v1+x/v2

2Average velocity =Distancetime/time

Hope it Heplfull Answer

Answer 2

Let the total distance travelled is S

Let the time taken for 1st half interval be t1 and for 2nd half interval be t2.

for the first half distance, $\sf\dfrac{S}{2}$, time t1 = $\sf\dfrac{\frac{s}{2}}{v_0}$ = $\sf\dfrac{s}{2v_0}$

t1 = $\sf\dfrac{s}{2v_0}$

Let the total time taken to travel the remaining distance be t2.

.•. $\sf\dfrac{s}{2}$ = $\sf\dfrac{t_2v_1}{2}+ \dfrac{t_2v_2}{2}$

S = t2(v1 + v2)

t2 = $\sf\dfrac{s}{v1 + v2}$

Therefore, total time = t1 + t2

= $\sf\dfrac{s}{2v_0} + \dfrac{s}{v_1 + v_2}$

Total distance = S

Average speed = $\sf\dfrac{total\: distance} {total\: time}$

= $\sf\dfrac{S}{\frac{s}{2v_0} + \frac{s}{v_1+v_2}}$

Average speed = $\dfrac{2v_0(v_1+v_2)}{v_1 + v_2 + 2v_0}$

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