Question Video: Calculating the Average Velocity of a Car | Nagwa Question Video: Calculating the Average Velocity of a Car | Nagwa

Question Video: Calculating the Average Velocity of a Car Physics • First Year of Secondary School

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A car is moving from point ๐ด to point ๐ท as shown in the diagram below. The car moves from ๐ด to ๐ต in 100 s, then from ๐ต to ๐ถ in 40 s, and then from ๐ถ to ๐ท in 60 s. Calculate the magnitude of the carโ€™s average velocity.

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Video Transcript

A car is moving from point ๐ด to point ๐ท as shown in the diagram below. The car moves from ๐ด to ๐ต in 100 seconds, then from ๐ต to ๐ถ in 40 seconds, and then from ๐ถ to ๐ท in 60 seconds. Calculate the magnitude of the carโ€™s average velocity.

Letโ€™s begin by recalling that the average velocity, ๐‘ฃ, of an object is given by the formula ๐‘ฃ equals ฮ”๐‘  divided by ฮ”๐‘ก, where the object has some displacement ฮ”๐‘  over a time interval ฮ”๐‘ก. Itโ€™s important to remember that the displacement of the car, ฮ”๐‘ , is simply the straight-line distance from its starting point to its ending point. So, although the car drove along this entire path to get from point ๐ด to point ๐ท, this does not correspond to its displacement. Rather, its displacement is simply along the straight line connecting points ๐ด and ๐ท, shown here with a dashed line.

Note that if we were to use the total distance that the car traveled all the way from point ๐ด to ๐ต to ๐ถ then ๐ท, we would be calculating its average speed rather than its average velocity. So in order to answer this question correctly, we need to be careful to use the carโ€™s displacement, rather than the total distance it traveled.

Now, the carโ€™s paths along the first and third leg of its overall journey are parallel. Thus, if we were to connect all four points ๐ด through ๐ท, weโ€™d make a parallelogram. Because of this, we can take the magnitude of the carโ€™s displacement to be 0.8 kilometers. Therefore, we know that ฮ”๐‘  equals 0.8 kilometers. Itโ€™ll be a good idea to convert the displacement value from kilometers to plain meters. That way, weโ€™ll end up with a final velocity value in meters per second. We know that a kilometer equals 1000 meters. So, 0.8 kilometers equals 800 meters. So, we know that ฮ”๐‘  equals 800 meters.

Next, to find ฮ”๐‘ก, the time interval, we just need to add up the total time that it took for the car to get from point ๐ด to point ๐ท. The time taken during the first, second, and third part of the carโ€™s overall journey was 100 seconds, 40 seconds, and 60 seconds, respectively. So, adding them together, we find that ฮ”๐‘ก equals 200 seconds.

Now that we have values for ฮ”๐‘  and ฮ”๐‘ก, letโ€™s go ahead and substitute them in to the formula for velocity. We find that the carโ€™s average velocity is equal to 800 meters divided by 200 seconds. Finally, evaluating this expression, we get a result of four meters per second, and this is our final answer. We have found that the average velocity of the car is four meters per second.

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