First slide

Average Velocity

Question

A body, moving in a straight line, covers half the distance with a speed V, the remaining part of the distance was covered with a speed $V_{1}$ for half of the time and with a speed $V_{2}$ for the other half of the time. What is the average speed of the body?

Difficult

A

$\frac{V (V_{1} + V_{2})}{(2 V + V_{1} + V_{2})}$
B

$\frac{2 V (V_{1} + V_{2})}{(2 V + V_{1} + V_{2})}$
C

$\frac{2 V_{1} V_{2}}{(V + V_{1} + V_{2})}$
D

$\frac{V_{1} V_{2}}{(V + V_{1} + V_{2})}$

Solution

$\frac{t}{2} = \frac{S_{1}}{V_{1}} = \frac{S_{2}}{V_{2}} S_{1} = V_{1} \frac{t}{2} S_{2} = V_{2} \frac{t}{2} a v e r a g e v e l o c i t y f o r t h e s e c o n d h a l f = (S_{1} + S_{2}) / t = \frac{V_{1 +} V_{2}}{2} o v e r a l l a v e r a g e v e l o c i t y$
$∴ (V) = \frac{S}{\frac{\frac{S}{2}}{V} + \frac{S}{V_{1} + V_{2}}} = \frac{2 V (V_{1} + V_{2})}{2 V + V_{1} + V_{2}}$

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