The position (in thousands of feet) of a car driving along a straight road at time t in minutes is given by the function y = s(t) that is pictured below.

Question

The position (in thousands of feet) of a car driving along a straight road at time t in minutes is given by the function y = s(t) that is pictured below.

Let v(t) denote the velocity of the car (in thousands of feet per minute) at time t (in minutes). Which graph A-F is the best representative of the derivative function v'(t)?

A		B		C
D		E		F

Which of the following statements is true? Select all that apply.

A. There are times when v'(t) is zero and v(t) is not zero.

B. When v'(t) is negative, the car is moving backward.

C. When v(t) is positive, v'(t) must also be positive.

D. If v'(t) is zero, then v(t) must be zero.

E. The function v' represents the position of the car.

F. The function v' represents the acceleration of the car.

G. When v'(t) is negative, the car is slowing down.

H. None of the above statements are true.

Answer 1

velocity is zero and acceleration = zero when s(6)=0.

that narrows it down to either B or C

the graphs are of acceleration, v'(t)=a(t) which have intervals where they are negative. v(t) though is always positive or zero from the s(t) graph. So C is correct. If your screen is small, eyesight not perfect, you may miss the tiny ' apostrophe on the v'(t)

A is true, as acceleration can be zero when velocity is positive or any value.

B is false. Acceleration can be negative which means slowing down, but velocity can be any value, positive, zero or negative

C is false

D is false if acceleration is zero, velocity can be any value, it's just constant at that value

E is false. s(t) represents the position of the car. v'(t) represents acceleration

F is true the derivative of v(t) = v'(t) = a(t) = acceleration

G is true. when acceleration <0, the car is slowing down (maybe) if you consider going backwards at 10mph to backwards at 20 mph as "slowing down" the velocity is getting smaller, but the speed is increasing

H is false as at least as at least A and F are true, and probably G

"slowing down" is not a technical term like "speed" or "velocity" There's a distinction, depending on which you use, G is true or could be false.