The position of an airplane is described by the function . How long does it take the airplane to travel ?

The position of a person running is described by the function . How long does it take the person to run miles?

Find how long it takes for a projectile starting at to hit a critical point if its height is given by:

The velocity of a rocket shot into the air is described by the function . How long does it take the rocket to reach its highest point?

Suppose the acceleration function of a biker going uphill at the start of a race is , where is in seconds. When will it take the biker to reach constant velocity?

The position of a particle is defined by s(t) = 4t3 – 3t2 + 2t. At what time (to the nearest hundreth) is its velocity equal to 384?

A ball is thrown in the air, modeled by the function . At what time will the ball hit the ground?

There are equations in physics that can tell you about the position and velocity of an object as a function of time. If we were to graph the equation of the relationship between the object's height and time it would be a quadratic while graphing the velocity vs time would be linear (since velocity is the derivative of position in respect to time. The equation of the height of the projectile with respect to time is the following where is the initial height, is the acceleration, and is the initial velocity.

Say you throw a ball straight up in the air at an initial velocity of 20m/s. At approximately what time does the ball reach it's highest height? Use as the approximation for the acceleration due to gravity.

Assume the acceleration due to gravity is

If you throw a ball straight up with an initial velocity of how many seconds will it take before the ball returns to your hand?

A particle's velocity is modeled (in feet per second) by the equation:

At , the particle is at rest.

At what time is the particle's acceleration equal to 578 ft/s/s?