If a ball is given a push so that it has an initial velocity of 5 m/s down a certain inclined plane, then the distance it has rolled after t seconds is given by the following equation. s(t) = 5t + 4t^2 (a) Find the velocity after 2 seconds.
(b) How long does it take for the velocity to reach 35 m/s? (Round your answer to two decimal places.)

a. v = 21 m/s

b. t = 3.75 secs

Step-by-step explanation:

The initial velocity when the ball was pushed along the inclined plane is 5 m/s .The distance function with respect to time is given as s(t) = 5t + 4t².

The velocity is the derivative of displacement with respect to time. Mathematically, v = ds/dt

we have to differentiate the function   s(t) = 5t + 4t².

s(t) = 5t + 4t²

v(t) = 5 + 8t

replacing t = 2 secs in the velocity function

v(t) = 5 + 8(2)

v = 21 m/s

b. The time it take for the velocity to reach 35 m/s can be computed with the derived velocity formula

v(t) = 5 + 8t

35 = 5 + 8t

35 - 5 = 8t

30 = 8t

t = 30/8

t = 3.75 secs

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step-by-step explanation:

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