Chapter 2 Describing Motion

. . . . . . . . . . . . . . 3.1 Picturing Motion Motion Diagram (p45) The Particle Model . . . . . . . . . . . . . . . . . . . . . . . . . (constant speed) (speeding up) (speeding up/slowing down)

3.2 Where and When Vectors and Scalars Coordinate Systems. The origin is the point where both variables have a value of zero. Usually the x-axis is horizontal and the y-axis vertical. Vectors and Scalars

Vector quantity - a quantity that has both magnitude and direction Vector - an arrow drawn to scale used to represent a vector quantity Scalar quantity - a quantity that has magnitude but not direction

Examples Speed……….. Velocity……... Acceleration.. Time…………. Distance……. Force……… scalar vector

---Addition of Vectors The sum of two or more vectors is called their resultant. To find the resultant of two vectors that are at angles to each other, we use the tip-to-tail method. ** Vector addition arrows ** Time Intervals and Displacement Displacement is vector – Distance is scalar. There is a difference!

Distance vs. Displacement You drive the path, and your odometer goes up by 8 miles (your distance). Your displacement is the shorter directed distance from start to stop (yellow arrow). What if you drove in a circle? start stop

3.3 Velocity and Accelaration Time interval is shown by t  means “change in” 3.3 Velocity and Accelaration ** Speed and velocity are similar except speed is scalar and velocity vector.

instantaneous velocity - the velocity that something has at any one instance (The terms instantaneous speed and avg. speed may also be used)

The average velocity for a trip might be 53 miles/hour. However, during this trip your instantaneous speed might have been 0 miles/hour at a stoplight or 70 miles/hour on the open road.

1. What is the average speed of a cheetah that sprints 100 meters in 4 seconds? 2. How about if it sprints 50 m in 2 s? *

What are the units of speed? miles/hour…………….mph meters/second……….m/s kilometer/hour……….km/h furlongs/fortnight?

If a car moves with an average speed of 60km/h for an hour, it will travel a distance of 60 km. (a) How far would if travel if it moved at this rate for 4 hours? (b) For 10 h? (c) Would if be possible for the car to have an average speed of 60km/h and never exceed a reading of 60km/h?

Velocity Velocity = {speed with a direction} Examples: 70 mph is a speed. 70 mph North is a velocity.

Acceleration Acceleration - rate of change in velocity due to change in speed or direction Example: 9.8 meters/second2 downward

"She moves at a constant speed in a constant direction.” Say the same sentence in fewer words. Answer: “She moves at constant velocity.”

The speedometer of a car moving to the east reads 100km/h The speedometer of a car moving to the east reads 100km/h. It passes another car that moves to the west at 100km/h. Do both cars have the same speed? Do they have the same velocity?

During a certain time, the speedometer of car reads a constant 60km/h. Does this indicate a constant speed? Constant velocity?

Kinematics Formulas For 1-D motion with constant acceleration: v = (vi + vf) / 2 a = v / t = (vf – vi) / t vf = vi + a t d = v t = ½ (vi + vf) t = ½ (vi + vi + a t) t d = vi t + ½ a t2 vf = vi + a t t = (vf – vi) / a d = vi t + a t2 vf2 = vi2 +2 a d

Velocity & Acceleration Sign Chart + - Moving forward; Speeding up Moving backward; Slowing down Moving forward; Slowing down Moving backward; Speeding up

Example Multiple-Choice Questions 1 Example Multiple-Choice Questions 1. The two measurements necessary for calculating average speed are (a) acceleration and time. (b) velocity and time. (c) distance and time. (d) distance and acceleration.

2. What is the average speed of a horse that gallops a distance of 10 kilometers in a time of 30 minutes? (a) 10km/h (b) 20km/h (c) 30km/h (d) more than 30km/h

3. What is the acceleration of a car that maintains a constant velocity of 100km/h for 10 seconds? (a) 0 km/h s (b) 10 km/h s (c) 10 m/s2 (d) 1000 km/h s

Free Fall Free fall is a state of falling free from air resistance and other forces except gravity.

Acceleration due to Gravity This acceleration vector is the same on the way up, at the top, and on the way down! Near the surface of the Earth, all objects accelerate at the same rate (ignoring air resistance). a = -g = -9.8 m/s2 9.8 m/s2 Interpretation: Velocity decreases by 9.8 m/s each second, meaning velocity is becoming less positive or more negative. Less positive means slowing down while going up. More negative means speeding up while going down.

For Free Fall... (a) you drop an object from rest at t=0. (b) velocity acquired = acceleration ´ time v = g t (c)

6. Dan drops a stone down a well and sees it hit the water 4 seconds later. Neglecting air resistance, how deep is this well? (a) 9.8 m (b) 19.6 m (c) 78.4 m (d) 156.8 m (e) 39.2 m

7. Dan drops a stone down a well and sees it hit the water 4 seconds later. Neglecting air resistance, what is the speed of impact of the stone? (a) 9.8 m/s (b) 19.6 m/s (c) 4.9 m/s (d) 78.4 m/s (e) 39.2 m/s

End of Chapter 3