Question

A train first travels for $30min$ with a velocity $30km{h}^{-1}$ and then for $40min$ with a velocity $40km{h}^{-1}$ in the same direction, calculate the average velocity of the train.

• A. $45.82km{h}^{-1}$
• B. $90.47km{h}^{-1}$
• C. $35.71km{h}^{-1}$
• D. $70.11km{h}^{-1}$

Answer 1

Answer: (C)

$35.71km{h}^{-1}$

Total time of journey

$t=t_1+t_2$

$\Rightarrow t=\frac{30+40}{60}=\frac{7}{6}h$

$\therefore$ Average velocity $=\frac{\text{Total displacement travelled (S)}}{\text{Total time of journey (t)}}$

Total displacement in $t_1$ is $s_1$:

$s_1=\frac{30}{60}\times 30$

$\Rightarrow s_1=15km$

Total displacement in $t_2$ is $s_2$:

$s_2=\frac{40}{60}\times 40$

$\Rightarrow s_2=26.66km$

Total displacement $s$ in time $t$:

$s=41.66km$

$V_{avg}=\frac{s_1+s_2}{t}$

$V_{avg}=\frac{41.66}{\frac{7}{6}}$

$V_{avg}=35.71km{h}^{-1}$