Question

If a ball is given a push so that it has an initial velocity of 3 m/s down a certain inclined plane, then the distance it has rolled after T seconds is given by the following equation: s(t) = 3t + 4t^2. A. Find the velocity after two seconds. B. How long does it take for the velocity to reach 40 m/s?

          If a ball is given a push so that it has an initial velocity of 3 m/s down a certain inclined plane, then the distance it has rolled after T seconds is given by the following equation: s(t) = 3t + 4t^2. 
A. Find the velocity after two seconds.
B. How long does it take for the velocity to reach 40 m/s?
        
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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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If a ball is given a push so that it has an initial velocity of 3 m/s down a certain inclined plane, then the distance it has rolled after T seconds is given by the following equation: s(t) = 3t + 4t^2. A. Find the velocity after two seconds. B. How long does it take for the velocity to reach 40 m/s?
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Transcript

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00:01 The idea with this problem is that they give you the equation, or t squared, and the derivative of that equation is going to give you the velocity.
00:15 So hopefully you've already learned the product power rule, where you just move the coefficient in front, the exponent in front to multiply by the coefficient.
00:26 So four times two is eight, and that's t to the first power, which you don't actually have to write to the first power.
00:32 So now is where we split it up.
00:34 So with part a, what you have to do is figure out the velocity after two seconds.
00:40 So it's 3 plus 8, and you substitute 2 in for t.
00:44 And i hope you can do that in your head...
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