Question

A powerful motorcycle can accelerate from rest to 26.8 m/ s (100 km/h) in only 3.90 s. (a) What is its average acceleration? (b) How far does it travel in that time?

- $6.87\textrm{ m/s}^2$
- $52.3 \textrm{ m}$

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This is College Physics Answers with Shaun Dychko. This motorcycle starts from rest— we are told— so that means the initial velocity is zero; it has a final velocity of 26.8 meters per second and it accelerates during a time of 3.90 seconds. So we write down all this information that we are given. Part (a) asks us to find the average acceleration so we take the change in velocity, divide that by time, that's equation 10 in chapter 2. So that's 26.8 meters per second— final velocity— minus the initial velocity of zero divided by 3.90 giving an acceleration of 6.87 meters per second squared. And part (b) asks us how far did it go and there are two ways that we could answer this question; you might consider equation [2.53] which says that the final position is the initial position which we assume is zero, we could have written that up here as well, plus the initial velocity times time plus one-half times acceleration times time squared and this term would be zero, this term would be zero— this term is zero because it has an initial velocity of zero— and we found the acceleration in part (a) and we could plug that into here multiply by time squared, which we know, and get our answer. But I discourage using this formula because you are using a number that you calculated in this formula and if you made a mistake with this calculation, subsequent calculation's using that will also be a mistake. So let's use a formula that uses the raw data that we are given instead. So I'm using equation [2.50] because we can figure out the average velocity because we know what the initial and final velocities are and we are given the time and we know that the initial position is zero so this uses raw data instead of using numbers that we have calculated before. So we plug in this formula for average velocity here and so we have that the final position is the initial position plus the average velocity times time. So that's 0 meters—initial position—plus 0 meters per second—initial velocity—plus 26.8 meters per second—final velocity— divided by 2 times 3.90 seconds giving 52.3 meters will be the distance that it travels.