Question

A bus travels the first one third distance at a speed of $10km{h}^{-1}$, the next one third distance at a speed of $20km{h}^{-1}$ and the next one third distance at a speed of $30km{h}^{-1}$ .

• A. $20{ms}^{-1}$
• B. $\frac{50}{11}{ms}^{-1}$
• C. $\frac{180}{11}{ms}^{-1}$
• D. $30{ms}^{-1}$

Answer 1

The correct option is B $\frac{50}{11}{ms}^{-1}$

Let total distance is $d$ $km$.

Using $s=ut$ $\Rightarrow t_1=\frac{\frac{d}{3}}{10}=\frac{d}{30}$ hours,

$\Rightarrow t_2=\frac{\frac{d}{3}}{20}=\frac{d}{60}$ hours,

$\Rightarrow t_3=\frac{\frac{d}{3}}{30}=\frac{d}{90}$ hours,

$\text{Average speed}=\frac{\text{Total distance}}{\text{Total Time}}$

Average speed$=\frac{d}{\frac{d}{30}+\frac{d}{60}+\frac{d}{90}}=\frac{180}{11}kmh=\frac{50}{11}m{s}^{-1}$