Drag racer acceleration The fastest drag racers can reach a sp...

Question

Drag racer acceleration The fastest drag racers can reach a speed of 330 mi/hr over a quarter-mile strip in 4.45 seconds (from a standing start). Complete the following sentence about such a drag racer: At some point during the race, the maximum acceleration of the drag racer is at least _____ mi/hr/s. .

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says a cyclist goes from a standstill to a speed of 45 kilometers per hour in 15 seconds. Calculate the minimum value of the cyclist's maximum acceleration during this period in kilometers per hour per second. We're given 4 possible choices as our answers. For choice A, we have A is equal to 3 kilometers per hour per second. For choice B, we have A is equal to 5 kilometers per hour per second. For choice C, we have A is equal to 13 kilometers per hour per second. And for choice D, we have A is equal to 8 kilometers per hour per second. Now we're asked to calculate the minimum value of the cyclist's maximum acceleration during this time period. And so we need to recall our definition for acceleration. So our acceleration A is going to be equal to our final speed, which we'll label as V minus our initial speed, which we'll label as U, and that quantity is divided by the time interval over which the speed is changed, so we'll label that as T. So now we need to identify our values for our variables of V, U, and T. So, we'll start off with V and V is our final speed that we're going to achieve, and we're told the problem that the cyclist reaches a final speed of 45 kilometers per hour. Now U is going to be our initial speed, and we're told that the cyclist starts from a standstill. So starting from a standstill means that you're not moving. That means your speed is going to be 0 kilometers per hour. So U is equal to 0 kilometers per hour. Then finally, we need to identify T, which is the time interval over which this change happened, and we're told that that occurs in 15 seconds. So T is equal to 15 seconds. So now we can substitute these values back into our definition for acceleration. So we'll have A is equal to, or V we'll have 45 kilometers per hour. Minus U, which is 0 kilometers per hour, and that whole quantity is divided by T, which is 15 seconds. So evaluate this expression, this is going to be equal to 3 kilometers per hour per second. And so this is the answer that we're actually looking for, and this is indeed the minimum value of the cyclists maximum acceleration during this time period. Since if we chose a value that is smaller than this and applied it over the entire 15 2nd time interval, then we would not be able to reach our final speed of 45 kilometers per hour from a standstill. So this does give us the minimum value of the cyclist's maximum acceleration. So now that we have our final answer, we can compare it to our answer choices, and we see that the correct answer choice corresponds to answer choice A. So I hope that this explanation has been useful, and I'll see you in the next video.

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