Question

A car travels 30 km at a uniform speed of 40 km per hour and next 30 km at a uniform speed of 30 kilometr
e per hour. Find its average speed and average velocity

Answer 1

$\large\underline{\bigstar \: \: {\sf Given-}}$

• Car travels 30km at uniform speed ${\sf (v_1)= 40\:km/h}$ and next 30km uniform speed of ${\sf (v_2)=30\:km/h}$

$\large\underline{\bigstar \: \: {\sf To \: Find -}}$

• Average Speed
• Average Velocity

$\large\underline{\bigstar \: \: {\sf Formula \: Used -}}$

$\color{violet}\bullet\underline{\boxed{\sf Average \: Speed=\dfrac{Total \: Distance }{Total\: Time}}}$

$\color{violet}\bullet\underline{\boxed{\sf Average\: Velocity=\dfrac{Displacement}{Total\:Time}}}$

$\large\underline{\bigstar \: \: {\sf Solution-}}$

❏ $\underline\color{darkblue}{\rm Average \: Speed-}$

Total Distance (s)

$\implies{\sf s=30+30}$

$\color{orange}\implies{\sf s=60\:km }$

Total Time (T)

$\implies\boxed{\sf Time=\dfrac{Distance}{velocity} }$

$\implies{\sf t_1=\dfrac{s_1}{v_1} }$

$\implies{\sf t_1=\dfrac{30}{40}}$

$\color{orange}\implies{\sf t_1=\dfrac{3}{4} \:s}$

$\implies{\sf t_2=\dfrac{s_2}{t_2}}$

$\implies{\sf t_2=\dfrac{30}{30} }$

$\color{orange}\implies{\sf t_2=1\:s }$

$\implies{\sf T=t_1+t_2 }$

$\implies{\sf T=\dfrac{3}{4}+1 }$

$\implies\color{purple}{\sf Total \: Time (T)=\dfrac{7}{4}\:s}$

$\implies{\sf Average \: Speed=\dfrac{60}{\dfrac{7}{4}} }$

$\color{red}\implies{\sf Average \: Speed=34.2\:km/h}$

❏ $\underline\color{darkblue}{\sf Average \: Velocity-}$

Displacement-

Shortest distance Travelled it's also 60km

$\implies{\sf Average \: Velocity=\dfrac{60}{\dfrac{7}{4} }}$

$\implies{\sf Average \: Velocity=34.2\:km/h}$

$\large\underline{\bigstar \: \: {\sf Answer-}}$

Average speed = 34.2 km/h

Average velocity = 34.2 km/h