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kari74 [83]
3 years ago
7

A ball rolls down an inclined plane such that the distance (in centimeters) that it rolls in t seconds is given by s(t) = 2t^3 +

3t^2 + 4 for 0<=t<=3 At what time is the velocity 30cm/s?
Mathematics
1 answer:
IRISSAK [1]3 years ago
3 0
The ball's velocity will be represented by the derivative of its distance function:

s'(t)=6t^2+6t

Now find the times t for which this is equal to 30, i.e. solve

6t^2+6t=30\implies t^2+t-5=0

This has two solutions, t=-\dfrac{1\pm\sqrt{21}}2, but only one is positive and falls in the interval [0,3]. So the velocity reaches 30 cm/s when t=-\dfrac{1-\sqrt{21}}2\approx1.79.
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