The acceleration function a(t) (in m/s2) and the initial velocity v(0) are given for a particle moving along a line.
a(t)=2t+4,

v(0)=-5

(a) find the velocity v(t) at time t.

v(t)= ? m/s

(b) find the total distance d traveled during the time interval given above.

d=? m

A:

Step-by-step explanation:

Acceleration is second derivative of position, velocity is first derivative. Therefore, the velocity is the integral of acceleration.

Integrate:

V(0)=-5:

Therefore, v(t):

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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