AP Calculus Unit 4 Review (4.1-4.5)

Front

What is the formula for acceleration in terms of position function?

Back

Acceleration a(t) = d²x/dt², where x is the position function.

Front

How do you determine if a particle is moving to the right?

Back

If v(t) > 0, the particle is moving to the right.

Front

What is the relationship between volume and height for a rectangular box?

Back

Volume V = length × width × height; height increases as volume increases.

Front

How do you calculate the rate of change of volume for a spherical balloon?

Back

Volume V = (4/3)πr³; dV/dt = 4πr²(dr/dt).

Front

What is the formula for the volume of a sphere?

Back

Volume V = (4/3)πr³.

Front

What does it mean if the radius of a balloon is decreasing?

Back

The volume of the balloon is decreasing, calculated using dV/dt.

Front

How do you find the rate of change of height in a rectangular box?

Back

Use the formula: dH/dt = dV/dt / (length × width).

Front

What is the significance of the derivative in motion problems?

Back

The first derivative represents velocity, and the second derivative represents acceleration.

Front

How do you find the acceleration of an object from its position function?

Back

Differentiate the position function twice with respect to time.

Front

What is the relationship between the rate of change of radius and volume for a sphere?

Back

As the radius increases, the volume increases at a rate proportional to r².