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1. The current flowing through an electric circuit is the derivative of the charge as a function of time. If the charge q is given by the equation q(t)=3t^2+2t-5, what is the current at t=0?

a. -5
b. 0
c. 2
d. 8

2. The equation for the position of an object at time t is represented by the equation f(t)=4t^2-2t. Which equation represents the instantaneous velocity at any given time, t?
a. v(t)=8t
b. v(t)=4t
c. v(t)=4t-2
d. v(t)=8t-2

3. The position of a train as it travels between two stations is described by the equation f(t)=90t^2+2t, where f(t) is the distance in miles and t is time in minutes. What is its average velocity between minutes 3 and 7?
a. 816 mi./min.
b. 902 mi./min.
c. 1,310 mi./min.
d. 4,424 mi./min.

4. The velocity of a car, in mph, is described by the equation v(t)=-t^2+15. Describe the acceleration of the car at 5 seconds.
a. The car is slowing down at a rate of 10 mi./h^2.
b. The car is speeding up at a rate of 10 mi./h^2.
c. The car is slowing down at a rate of 12 mi./h^2.
d. The car is speeding up at a rate of 10 mi./h^2.

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3 answers

  1. 1.C
    2.D
    3.B
    4.A

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  2. Hey, you try first. You are supposed to know how to take the derivative of a polynomial.
    if y = a x^n
    then dy/dx = n a x^(n-1)

    and the derivative of a constant is therefore 0
    because if
    y = a x^0
    dy/dx = a * 0 * x^-1 = 0
    so if
    v = -t^2+15
    then
    a = dv/dt = -2 t + 0
    and at t = 5
    a = -2(5) = -10
    if dv/dt is negative and v is positive, it is slowing.

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  3. did you ever get the answers to this i really need them.

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