Rock Motion and Velocity Problems

This video tutorial focuses on vertical motion as it relates to calculus, applicable to physics problems. It covers the position, velocity, and acceleration functions, explaining how derivatives and integrals are used to transition between them. The video introduces the general form of the position function and discusses the impact of units on the formula. A practical problem is solved, involving a rock dropped from a building, to determine position and velocity functions, instantaneous and average velocity, and time to impact. The tutorial concludes with a discussion on speed versus velocity.

What is the derivative of the position function used to find?

• Velocity function

• Time function

• Acceleration function

• Position function

In the position function formula, what does the term '1/2 a t^2' represent?

• Initial velocity

• Acceleration effect over time

• Final velocity

• Initial position

When using the formula with 16t^2, what unit is the position measured in?

• Meters

• Feet

• Seconds

• Kilometers

What is the initial velocity of the rock when it is simply released from rest?

• 32 feet per second

• 9.8 meters per second

• 16 feet per second

• 0 feet per second

How do you calculate the instantaneous velocity at a specific time?

• Integrate the acceleration function

• Differentiate the position function

• Differentiate the velocity function

• Integrate the position function

What is the average velocity of the rock between 2 and 4 seconds?

• -96 feet per second

• 96 feet per second

• 0 feet per second

• 32 feet per second

How long does it take for the rock to hit the ground?

• 9.35 seconds

• 9.68 seconds

• 10 seconds

• 8.5 seconds

What is the speed of the rock just before it hits the ground?

• 309.8 feet per second

• -309.8 feet per second

• 32 feet per second

• 0 feet per second

What is the height of the rock 5 seconds after it was dropped?

• 900 feet

• 1200 feet

• 1000 feet

• 1100 feet

At what time will the rock be 100 feet above the ground?

• 9.35 seconds

• 9.68 seconds

• 8.5 seconds

• 10 seconds