Question

A car moving on a straight road covers first $1000\text{s}$ of its journey with speed of $18\text{km/h}$ and next $2000\text{s}$ of its journey with speed of $36\text{km/h}$. Average speed of the car during whole journey is

• A. $18\text{km/h}$
• B. $36\text{km/h}$
• C. $27\text{km/h}$
• D. $30\text{km/h}$

Answer 1

The correct option is D $30\text{km/h}$

Given data:
$V_1=18km/h,t_1=1000s$
$\Rightarrow t_1=1000/3600h$
$V_2=36km/h,t_2=2000s$
$\Rightarrow t_2=2000/3600h$


Assume the distance covered in two steps be $d_1$ and $d_2$.
Average speed: $V=\frac{totaldistane}{totaltime}$
$V=\frac{d_1+d_2}{t_1+t_2}$
$V=\frac{V_1.t_1+V_2.t_2}{t_1+t_2}$

$V=\frac{18\times \frac{1000}{3600}+36\times \frac{2000}{3600}}{\frac{1000}{3600}+\frac{2000}{3600}}$

$V=\frac{5+20}{5/6}=6\times 5=30km/h$

Alternate Method:

If you divide the total time travel into equal intervals, such that you know the speed in each interval, you can use the formula for average speed.
$V=\frac{V_1+V_2+V_3+....+V_n}{n}$

$\Rightarrow V=\frac{V_1+V_2+V_3}{3}$

$V=\frac{18+36+36}{3}=\frac{90}{3}=30km/h$