Speed and AccelerationMotion

Speed and Acceleration What is time?• A particular moment (EX: 3:30 pm) or an interval of time

(EX: the race lasted 30 minutes)• Measured in hours, minutes, days years• Scientists measure in seconds• Must have a number and a unit

Time measurements• How many seconds are in a minute?• How many minutes are in an hour?• How many hours are in a day?• How many days are in a year?• How many year are in a century?

What is distance? How far it is from one point to another

Motion and Position• Position –location of an object• A reference point is needed to determine the

position of an object • Motion occurs when an object changes its

position relative to a reference point. Therefore, movement is compared to a reference point

• Are you moving now? Compared to what?• A frame of reference is a coordinate system in

which the position of the object is measured.

Distance• An important part of describing the motion of

an object is to determine the distance in which an object has moved.

• Distance is a measure of how far it is from one point to another, how far something has moved.

• Measured in units of length• English system = inches, feet and miles• Metric system (SI units)= Millimeters,

centimeters, meters and kilometers• 1 m = 100 cm: 1 kilometer = 1000m

What SI unit would you use?• What unit would you use to measure the

distance home?• What unit would you use to measure your

height?• What unit would you use to measure your hand

span?• What unit would you use to measure the width

of your pencil lead?

Displacement• Displacement is the distance and direction of

an objects change in position from the starting point.

• Quick Question: How are distance and displacement different?

Speed

• Speed is the distance an object travels per unit of time. A measure of how quickly an object moves from one place to another. It is the rate at which distance is traveled or rate of change in position. Objects that are not moving are said to have a speed of 0 m/s.

• Any change over time is called rate.• Speed is the rate at which distance is traveled

or the rate of change in position

Calculating Speed• You need the distance traveled and the time

taken to travel that distance• Speed (S or V) = distance(d)/time(t) Units for Speed• Speed = Meter per sec (m/s), Miles per hour

(mi/hr), inches/second• Distance = meters (m), kilometer (km), miles

(mi)• Time = seconds (s), hours (hr)

Speed Triangle

• S = speed• D = distance• T = time

Practice Problem: Calculating Speed

• Formula: Distance traveled divided by the time taken.

• If you drove 90 miles in 1.5 hours, what is your speed for the trip?

Solving for other variables:• How far would you drive if you drove for 2

hours at 60mph?

Practice Problems

• 1. Nascar driver, Jeff Gordon, has a car that is one of the fastest on the circuit. If it travels 600 miles in 4 hours, what is his cruising speed?

Problems1. Nascar driver, Jeff Gordon, has a car that is one

of the fastest on the circuit. If it travels 600 miles in 4 hours, what is his cruising speed?

• v = d/t• V = 600 mi/4 hrs• V = 150 mi/hr

• 2. The fastest car on Earth, a German-made Thrust SSC, would win every Nascar race in America. If it takes 0.5 hours (30 minutes) to travel 380 miles, what is its speed?

2. The fastest car on Earth, a German-made Thrust SSC, would win every Nascar race in America. If it takes 0.5 hours (30 minutes) to travel 380 miles, what is its speed?

• v = d/t• v = 380 mi/ 0.5 hr• v = 760 mi/h (mph)

• 3. The fastest train on Earth, the TGV from France, can travel at faster speeds than trains in the United States. During a speed test, the train traveled 800 miles in 2.5 hours. What is its speed?

3. The fastest train on Earth, the TGV from France, can travel at faster speeds than trains in the United States. During a speed test, the train traveled 800 miles in 2.5 hours. What is its speed?

• v = d/t• v = 800 mi/ 2.5 hr• v = 320 mi/h (mph)

4. Spirit of Australia, a hydroplane boat, made speed records by traveling 239 miles in 0.75

hours (45 minutes). What is its record-breaking speed?

4. Spirit of Australia, a hydroplane boat, made speed records by traveling 239 miles in 0.75

• hours (45 minutes). What is its record-breaking speed?

• v = d/t• v = 239 mi/ 0.75 hr• v = 318.67 mi/h (mph)

5. The fastest plane ever made, the Lockhead SR71, was able to travel 2200 miles per hour.

• Based on this speed, how far could it travel in: a. 2 hours? b. 3 hours? c. 5 hours?

5. The fastest plane ever made, the Lockhead SR71, was able to travel 2200 miles per hour.

• Based on this speed, how far could it travel in: a. 2 hours? b. 3 hours? c. 5 hours?

• D = S x t• D = 2200 mi/hr x 2 hr• D = ?

• 6. How much time does it take for a bird flying at a speed of 45 miles per hour to travel a distance of 1,800 miles?

6. How much time does it take for a bird flying at a speed of 45 miles per hour to travel a distance of 1,800 miles?

• t = d/v• t = 1800 mi /45 mi/hr• t = 40 hrs

• 7. A cheetah runs at 60 mph for a distance of 0.5 miles. How long does this take? Change answer to seconds.

7. A cheetah runs at 60 mph for a distance of 0.5 miles. How long does this take? Change answer to seconds.

• t = d/v• t = 0.5 mi/ 60mph• t = 0.008 hr

• 0.008 hr x 60 sec = 0.48 secs 1hr

8. A comet is cruising through the solar system at a speed of 50,000 kilometers per hour for 4 hours time. What is the total distance traveled by the comet during this time?

8. A comet is cruising through the solar system at a speed of 50,000 kilometers per hour for 4 hours time. What is the total distance traveled by the comet during this time?

• d = vt• d = 50,000 km/h X 4 hrs• d = 200,000 km

• 9. A runner runs 6.9 mph for 54 minutes. What distance did the runner travel?

9. A runner runs 6.9 mph for 54 minutes. What distance did the runner travel?

• d = vt• d = 6.9 mph X 54 min• d = 372.6 mph/min (Does this make sense)• Must change minutes to hours• 54 min X 1 hour = 0.9 hr

60 min• d = 6.9 mph X 0.9 hr = 6.2 miles

Types of Speed• Constant speed = speed that is not

changing. Usually speed is not constant!

• Average speed – total distance traveled divided by the total time of travel, average of all speeds over time traveled. Example: Distance to San Antonio, Texas = 1000 miles. Time traveled = 15 hours. What is the average speed?

• Instantaneous speed – speed at a given point in time

GraphsGraphing Speed

• Distance - time graph or also called a position - time graph shows the motion of an object over a period of time.

• Time is plotted on the horizontal axis of the graph and distance traveled is plotted along the vertical axis

• Slope of a distance vs time graph or a position vs time graph will tell us the speed of an object

• Slope = rise (vertical) /run (horizontal)

• Label the Axis• Distance(position) is dependent variable • Time is the independent variable

Position vs Time Graph = SPEED

Distance vs Time Graph = SpeedDistance vs Time Graph = Speed

• Shows Shows distance traveled in relation to time traveleddistance traveled in relation to time traveled• Shows distance and direction of an object from its starting point.

Needs to be expressed with a number and a direction.• Line sloping upward – steady speed Line sloping upward – steady speed • Change in upward slope = changing speedChange in upward slope = changing speed

– Steeper = faster Steeper = faster • Flat line – no motionFlat line – no motion Downward slope – returning to startDownward slope – returning to start

Speed and Velocity

• We use the letter “V” to represent speed. The letter “V” stands for velocity

• Velocity = includes the speed and direction of an object

• Velocity can change even though the speed may not EX: Escalator in the mall

• Speed – tells you how fast you are going• Velocity – gives a speed along with a direction

Acceleration Speed and velocity• Acceleration is rate of change in velocity. When the velocity of

an object occurs, the object is accelerating. • Remember that velocity includes the speed and direction of an

object. Therefore acceleration occurs when an object changes its speed, its direction, or BOTH. It is the amount your speed increases compared to how long it took to increase

• Examples of acceleration: Speeding up, slowing down and

change direction• Speed increases- positive acceleration (acceleration)• Speed decreases – negative acceleration (deceleration)

• Example of changing direction: Fairs wheel, carousel, race car track. Turning a corner.

• Is acceleration occurring in these situations?

Calculating AccelerationAcceleration = Change in speed/change in time OR

Acceleration = (final velocity – initial velocity) / timea = v/t

Units for Acceleration• Acceleration = m/s2 , m/s/s, mi/hr/s, mi/hr2

• Velocity = m/s, mi/hr• Time = s, hr

• v = Vf - Vi

interval time

velocityof changeonaccelerati

a

v

t

• A negative acceleration means that the object is slowing down.

• EX: -20cm/sec2 means tha the speed is decreasing – this can also be referred to as deceleration

• Zero Acceleration – traveling at a constant speed in one direction

• Free Fall is 9.8m/s2 = accelerates at 9.8m/s for every second that it falls. This is the force of gravity pulling down on the object

Calculating Positive Acceleration • If a jet airliner reaches 80m/s at the end of the

run way in 20s. How much did the airliner accelerate if it started from rest?

Calculating Negative Acceleration• If a skateboarder is skating at a speed of 3m/s

and comes to a rest in 2 seconds. Calculate the acceleration.

Graph• Speed vs time Graph – shows how speed

changed with time – acceleration is the slope of the speed –time graph.

Speed Time graph = Acceleration

Speed vs Time Graph = Acceleration

Acceleration

• Acceleration occurs when an object accelerates (speeding up), decelerates (slowing down), or changes direction.

• The rate at which velocity changes

Speed- Time Graph

0

1

2

3

0 2 4 6 8 10

Time (s)

Sp

ee

d (

m/s

)

What is the acceleration between: 1.0-2s?2.2-3s?3.3-5s?4.5-10s?