Metric Prefixes Practice

1. If a radio wave has a period of 1 µs, what is the period in seconds?

2. A hydrogen atom has a diameter of about 10 nm.

– – Express this diameter in meters.

Express this diameter in millimeters.

– Express this diameter in micrometers.

3. The distance between the sun and Earth is about 1.5 X 10 11 m. Express this distance in kilometers and gigameters.

Frame of Reference

• • A system that defines where objects are for a problem.

For certain problems, there may be multiple frames of reference that can be used.

• Scalar

Scalar Vs. Vector

• Vector

Displacement

• • • • • Similar to distance, but displacement will also include the direction traveled.

Direction is indicated by a positive or negative number.

Positive means right or up and negative means left or down.

Equation: Δx=x f -x i Units:

Velocity

• • • • Similar to speed, but velocity also includes the direction traveled.

We will calculate average velocity using the Δ𝑥 equation, 𝑉 𝑎𝑣𝑔 = Δ𝑡 = 𝑥 𝑓 −𝑥𝑖 𝑡 𝑓 −𝑡𝑖 The sign conventions that we used for displacement also work for velocity.

Units:

Average Velocity Example

• During a race on level ground, Andra runs with an average velocity of 6.02 m/s east, what is her displacement after 137 s?

Average Velocity Problems

1. Heather and Matthew walk with an average velocity of 0.98 m/s east. If it takes them 34 minutes to walk to the store, what is their displacement?

2. If Joe rides his bicycle in a straight line for 15 minutes with an average velocity of 12.5 km/hr south, how far has he ridden?

Problems Continued

3. Simpson drives his car with an average velocity of 48.0 km/hr east. How long will it take him to drive 144 km on a straight road?

4. A bus travels 280 km south along a straight path with an average velocity of 88 km/hr south. The bus stops for 24 minutes. Then, it travels 210 km south with an average velocity of 75 km/hr south. How long does the total trip last? What is the overall average velocity?

Instantaneous Velocity

• • • • Instantaneous velocity can be found on a position vs. time graph.

It is the velocity at a given point in time.

It is found by finding the slope of the tangent line at that point of the graph.

Tangent line-

What is the instantaneous velocity at 1s, 3s, 4.2s and 7.3s?

Acceleration

• • Defined as the rate in change of velocity – It could be a change in speed and/or direction The following equation allows us to calculate average acceleration: – 𝑎 𝑎𝑣𝑔 = Δ𝑣 Δ𝑡 = 𝑣 𝑓 −𝑣𝑖 𝑡 𝑓 −𝑡𝑖 – Unit for acceleration:

Velocity and Acceleration

v i + + + or 0 0 a + + 0 + or 0 motion

speeding up speeding up slowing down slowing down constant velocity speeding up from rest at rest

Average Acceleration Example

• A shuttle bus slows down with an average acceleration of -1.8 m/s 2 . How long does it take the bus to slow from 9.0 m/s to a complete stop?

Average Acceleration Problems

1. A car traveling at 7.0 m/s accelerates uniformly at 2.5 m/s 2 to reach a speed of 12.0 m/s. How long does this take?

2. With an average acceleration of -1.2 m/s 2 , how long will it take to bring a bicycle at a speed of 6.5 m/s to a complete stop?

Problems Continued

3. Turner’s treadmill runs with a velocity of -1.2 m/s and speeds up at regular intervals during a half-hour workout. After 25 min, the velocity is -6.5 m/s. What is the average acceleration during this period?

4. Suppose a treadmill has an average acceleration of 4.7X10

-3 m/s 2 . How much will the speed change after five minutes? If the initial speed is 1.7m/s, what is the final speed?

Displacement With Constant Acceleration

• • • We will use several equations that include displacement, velocity, acceleration and time.

The first is below: ∆𝑥 = 1 2 (𝑣𝑖 + 𝑣𝑓)∆𝑡

Example

• A racing car reaches a speed of 42 m/s. It undergoes a constant acceleration and comes to a rest 5.5 s later. How far did the car take to stop?

Problems

1. A car accelerates uniformly from rest to a speed of 6.6 m/s in 6.5 s. Find the distance.

2. A driver in a car traveling at a speed of 21.8 m/s sees a cat 101 m away on the road. How long will it take for the car to accelerate uniformly to rest in 99 m.

3. A car enters the freeway with a speed of 6.4 m/s and accelerates for 3.2 km in 3.5 min. How fast is the car moving at the end?

Velocity and Displacement With Constant Acceleration

• • • You will use these equations when given the acceleration.

𝑣 𝑓 = 𝑣𝑖 + 𝑎∆𝑡 ∆𝑥 = 𝑣𝑖∆𝑡 + 1 2 𝑎 ∆𝑡 2

Example

• A plane at rest accelerates at 4.8 m/s 2 for 15 seconds and takes off. What is the speed at takeoff? How long must the runway be?

Problems

1. A car with an initial speed of 6.5 m/s accelerates at a uniform rate of 0.92 m/s 2 for 3.6 s. Find the final speed and displacement.

2. An automobile with an initial speed of 4.3 m/s accelerates at 3.0 m/s 2 . Find the final speed and displacement after 5.0 seconds.

Problems Continued

3. A car starts from rest and travels for 5.0 s with an acceleration of -1.5 m/s 2 . What is the final velocity? How far does it travel?

4. A car traveling at 15 m/s applies the brakes and accelerates at -2.0 m/s 2 . How long does it take to accelerate to 10 m/s? How far did the car travel?

Final Velocity After Any Displacement

• • This equation can be used when we don’t know the time.

𝑉 𝑓 2 = 𝑉𝑖 2 + 2𝑎∆𝑥 • Magnitude-

Example

• A person pushing a stroller starts from rest and accelerates at 0.5 m/s 2 . What is the velocity after 4.75 m?

Problems

1. A car traveling at 7.0 m/s accelerates at 0.8 m/s 2 for 245 m. What is the final velocity? What is the velocity after 125 m?

2. A car accelerates from rest at a rate of 2.3 m/s 2 . What is the speed after 55 m? How long does it take to travel 55 m?

Problems Continued

3. An aircraft has a liftoff speed of 33 m/s. What minimum acceleration does this require if the plane lifts off after 240 m?

4. A certain car is capable of accelerating at 0.85 m/s 2 . What is the magnitude of the car’s displacement as it accelerates from 83 km/hr to 94 km/hr?

Mixed Problems

1. Nathan accelerates his skateboard from rest to 12.5 m/s in 2.5 s.

a) What is his acceleration?

b) What is his displacement?

c) What is his average velocity?

2. Marissa’s car accelerates at a rate of 2.6 m/s 2 how long does it take to go from 24.6 m/s to 26.8 m/s?

Free Fall

• • • • • An object in free fall is falling toward the Earth and the only force acting on it is gravity.

Every object experiences the same acceleration due to gravity.

g= Also, since the acceleration is downward, g will be negative.

The acceleration is the same for an object going straight up.

Free Fall Example

• Jason hits a volleyball with an initial velocity of 6.0 m/s upward. If the ball starts 2 m above the floor, how long will it be in the air?

Assignment

• Page 64 1-4 1. a) -42 m/s b) 11 s 2. a) 22.1 m/s b) 2.25 s 3. a) 8.0 m/s 4. 1.8 m b) 1.63 s