Question

A car moves a distance of 200 m. It covers first half
of the distance at speed 60kmh
−1
and the second half
at speed u. If the average speed is 40kmh
−1
, the value
of u is
(1) 30 kmh−1

(2) 13 kmh−1

(3) 60 kmh−1

(4) 40 kmh−1

Answer 1

$\huge\underline\blue{\sf Answer:}$

$\large\red{\boxed{\sf u=30\:km/h}}$

$\huge\underline\blue{\sf Solution:}$

$\large\underline\pink{\sf Given: }$

• Total distance (s) = 200 m

On converting it in km (s) = 0.2 km

• Covers first half of the distance at at speed ($\sf{v_1}$) = 60km/h

• Covers second half distance at speed ($\sf{v_2}$)= u

• Average Speed ($\sf{V_{av}}$)=40km/h

$\large\underline\pink{\sf To\:Find: }$

• $\sf{v_2}$= u = ?

━━━━━━━━━━━━━━━━━━━━━━━━━

We know that ,

$\large{♡}$$\large{\boxed{\sf V_{av}={\frac{Total\: Distance}{Total\: Time}} }}$

Now ,

$\large{\sf t_1={\frac{0.1}{60}}}$

$\large{\sf t_2={\frac{0.1}{u}}}$

On putting value in the Formula we get,

$\large\implies{\sf 40={\frac{0.2}{0.1u+6/60u}}}$

$\large\implies{\sf 40=0.2×{\frac{60u}{0.1u+6}} }$

$\large\implies{\sf 40(0.1u+6)=0.2×60u}$

$\large\implies{\sf 4u+240=12u}$

$\large\implies{\sf 240=12u-4u }$

$\large\implies{\sf 240=8u}$

$\large\implies{\sf u={\frac{240}{8}}}$

$\large\implies{\sf u=30\:km/h }$

$\huge\red{♡}$$\large\red{\boxed{\sf u=30\:km/h}}$