Determine the rate of change of the angle opposite the base of a right triangle -whose length is increasing at a rate of 1 inch per minute, and whose height is a constant 2 inches - when the area of the triangle is 2 square inches.

A right triangle has sides of lenght and which are both increasing in length over time such that:

a) Find the rate at which the angle opposite is changing with respect to time.

The velocity of a car is given by the equation:

, where is the time in hours.

If the car starts out at a distance of 3 miles from its home, how far will it be after 4 hours?

A point on a circle of radius 1 unit is orbiting counter-clockwise around the circle's center. It makes one full orbit every 8 seconds. How fast is the coordinate changing when the line segment from the origin to the point, , forms an angle of radians above the positive x axis?

A spherical balloon is increasing in volume at a constant rate of . At a radius of 3 cm, what is the rate of change of the circumference of the balloon?

Soap is sometimes used to determine the location of leaks in industrial pipes. A perfectly spherical soap bubble is growing at a rate of . What is the rate of change of the surface area of the bubble when the radius of the bubble is ?

A pizzeria chef is flattening a circular piece of dough. The surface area of the dough (we are only considering the top of the dough) is increasing at a rate of 0.5 inches/sec. How quickly is the diameter of the pizza changing when the radius of the pizza measures 4 inches?

A man is standing on the top of a 10 ft long ladder that is leaning against the side of a building, when the bottom of the ladder begins to slide out from under it. How fast is the man standing on the top of the ladder falling when the bottom of the ladder is 6 ft from the building and is sliding at 2ft/sec?

The position of a car is given by the equation

.

Find the car's acceleration when .