Question

An object is moving along the x-axis. Its position at any time is given by: x(t) = 3cos(pit)+2. Find its acceleration.

Answer 1

Which of these physical settings makes sense for the object in Question 1:

a skydiver falling from a plane, before she opens her parachute
the shadow cast by a rock that's stuck on the edge of a spinning wheel
a car driving from San Diego to Los Angeles
an ant walking at a steady pace from the tip of a propeller toward the hub
none of these settings

Answer 2

Acceleration is the second derivative of the distance function.
x(t) = 3cos(pi*t)+2.
x'(t) = -3sin(pi*t)(pi) = -3pi(sin(pi*t))
x''(t)= -3pi * cos(pi*t)(pi) = -3pi^2 * cos(pi*t).

Answer 3

A science teacher has a supply of 50% sugar solution and a supply of 80% sugar solution. How much of each solution should the teacher mix together to get 150 mL of 60% sugar solution?
a. 70 mL of the 50% solution and 35mL of the 80% solution.
n. 35mL of the 50% solution and 70mL of the 80% solution.
c. 70mL of the 50% solution and 70mL of the 80% solution.
d. 35mL of the 50% solution and 35mL of the 80% solution.

Answer 4

To see which makes actual sense, try graphing the object's position, velocity, and acceleration. This function is a trigonometric function. It oscillates back and forth.

a skydiver falling from a plane, before she opens her parachute means that the distance is exponentially going farther and farther, as the velocity gets faster and faster, and the acceleration remains constant.
Can't be this.

the shadow cast by a rock that's stuck on the edge of a spinning wheel
Makes the most sense to me, because the shadow gets larger exponentially faster, and then suddenly gets smaller, and larger, and smaller, etc. because the wheel is spinning.

A car driving from San Diego to Los Angeles
The car would have to reach LA and then back to San Diego and then back to LA and then back and... no.

An ant walking at a steady pace from the tip of a propeller toward the hub
I don't think this makes sense, either, because the ant has a constant velocity, and as we saw with the velocity function, it's not constant. Sometimes it's negative, sometimes it's positive.

None of these settings
I hate when professors throw in this option.
To me, it's either the spinning wheel/rock answer, or this one.