Question

John drove south 120km at 60km/h and then east 150km at 50km/h.
Determine:
a. the average speed for the whole journey
b.the magnitude of the average velocity for the whole journey

Answer 1

Answer on question #61642, Physics, Solid State Physics

John drove south $120\mathrm{km}$ at $60\mathrm{km/h}$ and then east $150\mathrm{km}$ at $50\mathrm{km/h}$ . Determine:

a) The average speed for the whole journey.

b) The magnitude of the average velocity for the whole journey.

Solution:

a)

The time $t_1$ to cover $120 \, \text{km}$ at a speed of $60 \, \text{km/h}$ is given by

$$t _ {1} = \frac {1 2 0 k m}{6 0 k m / h} = 2 h o u r s$$

The time $t_2$ to cover $150 \, \text{km}$ at a speed of $50 \, \text{km/h}$ is given by

$$t _ {2} = \frac {1 5 0 k m}{5 0 k m / h} = 3 h o u r s$$

average speed $= \frac{\text{distanse}}{\text{time}}$

average speed $= \frac{120km + 150km}{2h + 3h} = 54km / h$

b)

The magnitude of the displacement is the distance AC between the final point and the starting point and is calculated using Pythagora's theorem as follows

$$A C ^ {2} = A B ^ {2} + B C ^ {2}$$ $$A C = \sqrt {1 2 0 ^ {2} + 1 5 0 ^ {2}} = \sqrt {1 4 4 0 0 + 2 2 5 0 0} = 3 0 \sqrt {4 1} k m$$ $$average velocity = \frac{displacement}{time}$$ $$average velocity = \frac{30\sqrt{41} \, \text{km}}{2 \, h + 3 \, h} \approx 38.4 \, \text{km/h}$$

Answer: a) $54 \, \text{km/h}$ b) $38.4 \, \text{km/h}$

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