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November 28th, 2015, 01:07 AM  #1 
Member Joined: Jun 2013 Posts: 42 Thanks: 0  how to find the distance given the velocity?
Starting at rest, the velocity of an object is given by v = 3t^2. Find the distance traveled after 5 seconds. My solution: d =vt but v = 3t^2 so: d = (3t^2)(t) @t=5 d = [3(5)^2](5) d = [3(25)](5) d = 75(5) d = 375 units My answer is obviously correct, but the answer in the book is d=125. Please tell me whether the book is wrong or I am wrong, If I am wrong, please explain why I am wrong... thank you. Last edited by skipjack; November 28th, 2015 at 01:35 AM. 
November 28th, 2015, 01:47 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,019 Thanks: 2254 
You are wrong. The equation d = vt applies if v is the mean velocity. In particular, this equation is correct if v is a constant. You are given that v = 3t². You need to use the fact that v is the derivative of d with respect to time. As d = 0 when t = 0, d = t³, and so d = 125 when t = 5. 

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distance, find, velocity 
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