First slide

Average Velocity

Question

A train moving at a constant velocity of 54 km/hr moves east wards for 30 minutes, then due north with the same speed for 40 minutes. What is the average velocity of the train during this run? (in km/hr)

Easy

A

30
B

35
C

38.6
D

49.3

Solution

$\large \overrightarrow d = \overrightarrow {{d_1}} + \overrightarrow {{d_2}}$
$\large \therefore |\vec d|=\sqrt{|\vec d_1|^2+|\vec d_2|^2}$
$\large \left| {\overrightarrow {{d_1}} } \right| = 54 \times \frac{{30}}{{60}} = 27km$
$\large \left| {\overrightarrow {{d_2}} } \right| = 54 \times \frac{{40}}{{60}} = 36km$
$\large \left| {\overrightarrow d } \right| = \sqrt {{{(27)}^2} + ({{36}^2})} = 45km$
Average velocity = $\large \frac{{45}}{{\left( {\frac{1}{2} + \frac{{40}}{{60}}} \right)}} = 38.6km/hr$

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