VelocityVelocityAndAndAccelerationAcceleration

Velocity: Both speed and Velocity: Both speed and direction of an object direction of an object V=d/t.V=d/t.

Acceleration: The rate at Acceleration: The rate at which velocity changes.which velocity changes.

AccelerationAcceleration

Speed and VectorSpeed and VectorA vector quantity has both A vector quantity has both

magnitude (the amount of magnitude (the amount of or how much of) and or how much of) and direction. Therefore direction. Therefore Velocity is a vector.Velocity is a vector.

Speed however only has Speed however only has magnitude not direction.magnitude not direction.

Displacement and VelocityDisplacement and Velocity Distance is the total length of the Distance is the total length of the

actual path between two points. actual path between two points. Displacement is the length and Displacement is the length and direction of a straight line direction of a straight line between starting and ending between starting and ending points.points. Therefore displacement is Therefore displacement is a vector. a vector.

Chapter 9 Motion and Energy

The arrows are larger as the plane increases speed or accelerates, because the arrows represent the vector quantity.

Types of Types of AccelerationAcceleration

1. Increasing speed: speed 1. Increasing speed: speed increases per unit of timeincreases per unit of time

2. Decreasing speed: speed 2. Decreasing speed: speed Decreases per unit of timeDecreases per unit of time

3. Changing 3. Changing Direction:turning or circles.Direction:turning or circles.

Equation for Equation for AccelerationAcceleration

Final Velocity-Beginning VelocityFinal Velocity-Beginning Velocity

TimeTime

Fv-Bvt

Beginning Velocity

Final Velocity

Time

a =

UnitsUnits

m/s/s or m/sm/s/s or m/s2

A car was traveling 10m/s A car was traveling 10m/s and increased its speed to and increased its speed to 20m/s in 2s. What was the 20m/s in 2s. What was the car's acceleration?car's acceleration?

1 2 3 4

25% 25%25%25%1.1. 30m/s/s30m/s/s

2.2. 10m/s/s10m/s/s

3.3. 5mph5mph

4.4. 5m/s/s5m/s/s

0

30

A car was traveling 10m/s A car was traveling 10m/s and decreased its speed and decreased its speed to 0m/s in 1s. What was to 0m/s in 1s. What was the car's acceleration?the car's acceleration?

1 2 3 4

25% 25%25%25%

0

30

1.1. -10m/s/s-10m/s/s

2.2. 10m/s/s10m/s/s

3.3. 9mph9mph

4.4. 9m/s/s9m/s/s

A bowling ball was A bowling ball was dropped from a building. It dropped from a building. It reached a speed of reached a speed of 19.6m/s in 2 seconds. 19.6m/s in 2 seconds. What was the car's What was the car's acceleration?acceleration?

1 2 3 4

25% 25%25%25%

0

30

1.1. -9.8m/s/s-9.8m/s/s

2.2. 19.6m/s/s19.6m/s/s

3.3. 18mph18mph

4.4. 9.8m/s/s9.8m/s/s

Graphing Graphing AccelerationAcceleration

What is this a graph of?What is this a graph of?

1 2

50%50%

1.1. SpeedSpeed

2.2. accelerationacceleration

Importance of Slope and Importance of Slope and MotionMotion The shapes of the distance vs. time graphs for constant The shapes of the distance vs. time graphs for constant

velocity motion and accelerated motion (i.e., changing velocity motion and accelerated motion (i.e., changing velocity) - reveal an important principle. The principle is velocity) - reveal an important principle. The principle is that the slope of the line on a distance vs. time graph that the slope of the line on a distance vs. time graph reveals useful information about the velocity of the reveals useful information about the velocity of the object. Whatever characteristics the velocity has, the object. Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa). If the slope will exhibit the same (and vice versa). If the velocity is constant, then the slope is constant (i.e., a velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing, then the slope straight line). If the velocity is changing, then the slope is changing (i.e., a curved line). If the velocity is is changing (i.e., a curved line). If the velocity is positive, then the slope is positive (i.e., moving positive, then the slope is positive (i.e., moving upwards and to the right). This very principle can be upwards and to the right). This very principle can be extended to any motion conceivable. extended to any motion conceivable.