100-m speed The Jamaican sprinter Usain Bolt set a world recor...

Question

100-m speed The Jamaican sprinter Usain Bolt set a world record of 9.58 s in the 100-meter dash in the summer of 2009. Did his speed ever exceed 30 km/hr during the race? Explain.

Accepted Answer

Hello. In this video, we will be approaching the following word problem. We are told that during a 150 m sprint, a runner completed the distance in 14.25 seconds. We are asked to answer, did the runner's speed ever exceed 36 kilometers per hour during the sprint? Let's go ahead and start by drawing a diagram of the given information. First, we are told that we have a sprint that covers a total distance of 150 m. We are told that a runner completes the entire distance in 14.25 seconds, and this problem asks us to verify if the runners speed ever went above 36 kilometers per hour. Now, there's two pieces of information that we know. Again, we know that the total distance of the track is 150 m, and we know that the speed or the time, sorry, I should say time, that this was completed in. Is 14.25 seconds. What this means is that we want to first calculate the average rate at which the sprinter completed the run. In order to find this, we are going to take the average velocity of the sprinter. The sprinter's average velocity will equal to the total distance. Divided by the time it took to complete the distance, this is going to give us 150 m divided by 14.25 seconds, and this will further simplify to give us 10.53 m per second. Now the question is to verify, does 10.53 m per second. Have a higher value than 36 kilometers per hour. Well, in order to answer this, first we need to convert 36 kilometers per hour into meters per second. In order to do this, we will take the units 36 kilometers per hour. And we'll first start by converting kilometers into meters. We know that there are 1000 m in 1 kilometer, so we will be multiplying this by 1000 m. Divided by 1 kilometer. Then we need to convert hours into seconds. We know that in 1 hour, there are a total of 3600 seconds. Now what we are going to do is we are going to simplify the following unit chain. So, we know that kilometers will cancel each other out, leaving us with meters in the numerator, and we know that our will cancel each other out, leaving seconds in the denominator. That will leave us with 36 multiplied by 1000 m, divided by 3600 seconds. This is going to further simplify to give us. 10 m per second. And based off the runner's average average velocity, 10.53 m per second is greater than 10 m per second. So that means that the runner's average velocity did exceed 36 kilometers per hour, and with that being said, the answer to this problem is going to be A. So, I hope this video helps you in understanding on how to approach this problem, and I will go ahead and see you all in the next video.

100-m speed The Jamaican sprinter Usain Bolt set a world record of 9.58 s in the 100-meter dash in the summer of 2009. Did his speed ever exceed 30 km/hr during the race? Explain.

Key Concepts

Speed Calculation

Unit Conversion

Average vs. Instantaneous Speed

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