Velocity and Acceleration. Definitions of Velocity and Acceleration.

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Presentation transcript:

Velocity and Acceleration

Definitions of Velocity and Acceleration

1. The position vector r describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the given point (Similar to p.856 #1-10) Position FunctionPoint (1, 2)

2. The position vector r describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the given point (Similar to p.856 #1-10) NEXT TIME Position FunctionPoint (4, 16)

3. The position vector r describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the given point (Similar to p.856 #1-10) Position FunctionPoint

4. The position vector r describes the path of an object moving in space. Find the velocity, speed, and acceleration of the object (Similar to p.856 #11-20)

5. The position vector r describes the path of an object moving in space. Find the velocity, speed, and acceleration of the object (Similar to p.856 #11-20)

6. The position vector r describes the path of an object moving in space. Find the velocity, speed, and acceleration of the object (Similar to p.856 #11-20)

7. Use the given acceleration function to find the velocity and position vectors. Then find the position at time t = 2 (Similar to p.856 #23-28)

8. Use the given acceleration function to find the velocity and position vectors. Then find the position at time t = 2 (Similar to p.856 #23-28)

9. Use the given acceleration function to find the velocity and position vectors. Then find the position at time t = 5pi/3 (Similar to p.856 #23-28)

Position Function for a Projectile

10. Use the model for projectile motion, assuming there is no air resistance (Similar to p.856 #29-44) Find the vector-valued function for the path of a projectile launched at a height of 20 feet above the ground with an initial velocity of 100 feet per second and at an angle of 45 o above the horizontal.

11. Use the model for projectile motion, assuming there is no air resistance (Similar to p.856 #29-44) A baseball, hit 5 feet above the ground, leaves the bat at an angle of 30 o and is caught by an outfielder 5 feet above the ground and 200 feet from home plate. What is the initial speed of the ball, and how high does it rise?