Question

a body covers half of the journey with speed a m/s and other half the speed b m/s calculate the average speed of body during the whole journey
​

Answer 1

s/2=a•t1

t1=s/2a

t2=s/2b

average speed=s/(s/2a+s/2b)

=1/(1/2a+1/2b)

=4ab/(2a+2b)

Answer 2

Let, total distance travelled = (2s) m

First speed = (a) m/s

Second speed = (b) m/s

We know,

$\boxed{v_{av} = \frac{Total \ ‘s’}{Total \ ‘t’}}$

Finding time when it was in speed (a) m/s:-

$t = \frac{s}{v}$

⇒ $t_1$ = (s/a) s

Finding time when it was in speed (b) m/s:-

⇒ $t_2$ = (s/b) s

Now putting the values,

$v_{av} = \frac{s + s}{t_1 + t_2}$

$\implies v_{av} = \frac{s + s}{\frac{s}{a} + \frac{s}{b}}$ m/s

$\implies v_{av} = \frac{2s}{\frac{sb+sa}{ab}}$

$\implies v_{av} = \frac{2s × ab}{s(a + b)}$

$\boxed{\implies v_{av} = (\frac{2ab}{a + b}) m s^{-1}}$ (answer).

More:-

Average speed when 3 speeds are given:-

$\boxed{(\frac{3abc}{ab + bc + ca})}$