Suppose a baseball is thrown vertically upward from the ground with an initial velocity of v₀ ft/s. The approximate height of the ball (in feet) above the ground after t seconds is given by s(t) = -16t² + v₀t.
With what velocity does the ball strike the ground?

Suppose a stone is thrown vertically upward from the edge of a cliff on Earth with an initial velocity of 32 ft/s from a height of 48 ft above the ground. The height (in feet) of the stone above the ground t seconds after it is thrown is s(t) = -16t² + 32t + 48.

With what velocity does the stone strike the ground?

Suppose a stone is thrown vertically upward from the edge of a cliff on Earth with an initial velocity of 32 ft/s from a height of 48 ft above the ground. The height (in feet) of the stone above the ground t seconds after it is thrown is s(t) = -16t² + 32t + 48.

On what intervals is the speed increasing?

Suppose a stone is thrown vertically upward from the edge of a cliff on Earth with an initial velocity of 19.6 m/s from a height of 24.5 m above the ground. The height (in meters) of the stone above the ground t seconds after it is thrown is s(t) = -4.9t² + 19.6t + 24.5.

On what intervals is the speed increasing?

Suppose a stone is thrown vertically upward from the edge of a cliff on Earth with an initial velocity of 64 ft/s from a height of 32 ft above the ground. The height (in feet) of the stone above the ground t seconds after it is thrown is s(t) = -16t² + 64t + 32.

On what intervals is the speed increasing?

Interpreting the derivative Find the derivative of each function at the given point and interpret the physical meaning of this quantity. Include units in your answer.

An object dropped from rest falls d(t)=16t² feet in t seconds. Find d′(4).

A feather dropped on the moon On the moon, a feather will fall to the ground at the same rate as a heavy stone. Suppose a feather is dropped from a height of 40 m above the surface of the moon. Its height (in meters) above the ground after t seconds is s = 40−0.8t². Determine the velocity and acceleration of the feather the moment it strikes the surface of the moon.

Position, velocity, and acceleration Suppose the position of an object moving horizontally along a line after t seconds is given by the following functions s = f(t), where s is measured in feet, with s > 0 corresponding to positions right of the origin.

b. Find and graph the velocity function. When is the object stationary, moving to the right, and moving to the left?

f(t) = 18t-3t²; 0 ≤ t ≤ 8

The position (in meters) of a marble, given an initial velocity and rolling up a long incline, is given by s = 100t / t+1, where t is measured in seconds and s=0 is the starting point.

b. Find the velocity function for the marble.