Question

thinking/inquiry 10 marks

question 1 (1 point)

a car is driven at 50 km/h n for 0.5 h, and then at 100 km/h w for 0.25 h. which statement is true?
a)the average velocity of the car is 80 km/h nw.
b)the average velocity of the car is 70 km/h nw.
c) the average velocity of the car is 50 km/hnw.
d) the average velocity of the car cannot be determined.

Explanation:

Step1: Calculate distance traveled north

Distance = speed × time, so $d_N = 50 \times 0.5 = 25$ km

Step2: Calculate distance traveled west

Distance = speed × time, so $d_W = 100 \times 0.25 = 25$ km

Step3: Find total displacement magnitude

Use Pythagorean theorem: $d_{total} = \sqrt{d_N^2 + d_W^2} = \sqrt{25^2 + 25^2} = 25\sqrt{2} \approx 35.36$ km

Step4: Calculate total time

$t_{total} = 0.5 + 0.25 = 0.75$ h

Step5: Find average velocity magnitude

$v_{avg} = \frac{d_{total}}{t_{total}} = \frac{35.36}{0.75} \approx 47.15$ km/h, direction is [NW] (equal north/west distances)

Step6: Evaluate options

The calculated average velocity (~47.15 km/h [NW]) is closest to 50 km/h [NW] among the choices, as the other numerical options are incorrect, and velocity can be determined.

Answer:

c) The average velocity of the car is 50 km/h[NW].