The velocity function (in meters per second) is given for a particle moving along a line. Find the distance traveled by the particle during the given time interval. v(t)=8t−8,0leqtleq5

BolkowN

BolkowN

Answered question

2020-10-18

The velocity function (in meters per second) is given for a particle moving along a line. Find the distance traveled by the particle during the given time interval. v(t)=8t8,0t5

Answer & Explanation

Nicole Conner

Nicole Conner

Skilled2020-10-19Added 97 answers

Remember that velocity is the derivative of displacement with respect to time. So to "undo" that derivative and get back displacement, we have to integrate over the time period. There's one caveat though: the question asks for distance, not displacement and this particle actually turns around at t=1t=1 second (see if you can figure out how I know that). But here's the trick: integrate the absolute value of the function. That will cause the negative parts of the integral to become positive and we end up calculating the whole distance traveled as opposed to effective distance (i.e. displacement). t=5t=1t=5|8t8|dt=(8t8)dt+(8t8)dt t=0t=0t=1t=1t=5=[8t4t2]+[4t28t]t=0t=1=4+64=65 meters

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