Speed, Acceleration and Momentum

Forces in Motion

Mrs. Rubel

Motion and Point of Reference

Motion is a change in position

Determining whether or not something has changed its position depends on your Point of Reference.

Your point of reference is where you are relative to the moving object.

Distance and Displacement

You know the distance from a starting point, but what is displacement?

Displacement is distance plus direction FROM THE STARTING POINT.

Displacment ExamplesYou move 20 meters north from your starting point:

Distance = 20 meters

Displacement = 20 meters North

You move 20 meters north, and then 18 meters south

Distance = 38 meters

Displacement = 2 meters North

You move 20 meters north and then 20 meters south

Distance = 40 miles

Displacement = 0! (why?)

SpeedSpeed is the rate that indicates how much

distance you traveled divided by the amount of time that you traveled. It is measured in meters per second (m/s).

Formula = distance (meters) time (seconds)

Example:You ran the 100 m dash in 20 seconds100 m20 s = 5 m/s (you traveled 5 meters every second you were running)

VelocityVelocity is the exact same formula as speed, but it has one big difference. VELOCITY IS THE SPEED PLUS THE DIRECTION YOU ARE TRAVELING.Use the example from before:

You ran the 100 m dash in 20 seconds100 m

20 s = 5 m/s W (you traveled 5 meter per second in a western direction)

Merry-Go-Round

Remember, velocity changes whenever you change your direction. So…

A merry-go-round can move at a constant speed of 20 miles/hour, but, because it is going in a circle (and changing direction), it can have a constant speed but changing velocity.

Average Speed vs. Constant Speed

Most of the time we calculate average speed (example: going to Grandma’s house). It is Total Distance / Total Time.

However, in some cases, an object travels at a constant rate when the speed never changes (do you have cruise control on your car?)

Average Speed Graph

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Graphing Average Speed

Suppose Grandma lived 240 miles away, and you traveled there in 4 hours. Your car probably traveled at different velocities (different speeds at different directions), and you may have made a few stops along the way. So your graph would not be a perfectly straight line.

Constant Speed

Let’s say that the road to Grandma’s was a straight line, and there were no stops or delays along the way. If you traveled at a constant speed of 60 mph, then a constant speed would be graphed as a straight line.

Graphing Constant Speed

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Acceleration

Most people think of acceleration as speeding up, but acceleration is actually a change in velocity over time.

Formula:Final Velocity – Starting Velocity

Time (sec) = m/s2

Or m/s/s

Acceleration

Acceleration can occur when

1) You are increasing your speed (positive acceleration)

2) You are decreasing your speed (negative acceleration or deceleration)

3) You are changing direction

Acceleration and Velocity

Even though velocity is the same as speed (and same formula) and

Acceleration is a change in speed (speeding up or slowing down)

Both velocity and acceleration change when you change direction.

So There are 3 Ways to Accelerate

1. Speed up (positive acceleration)

2. Slow down (negative acceleration or deceleration, or

3. Change your direction.

Acceleration Problems

You start off riding your bike at 5 m/s. Then you go down a big hill. At the bottom of the hill your are traveling at 15 m/s. It took you 5 seconds to go from the top of the hill to the bottom of the hill

1) What was your rate of acceleration?

2) Was it positive or negative acceleration?

Acceleration Problems

You are riding your bike at 20 m/s. You now are having to go uphill. You don’t exert more effort, so, by the time you reach the top of the hill, you are traveling at 10 m/s. It took you 10 seconds to go from the bottom of the hill to the top.1) Is this positive or negative acceleration?2) what was your rate of acceleration?

Don’t Drink Milk Before A Race

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Momentum

Momentum is really a measure of how difficult it is to stop a moving object. An object that collides with an object at rest (and bounces off )will have the same momentum as it had before.An object that collides with an object in motion will experience a momentum that is a combination of both moving objects.

Momentum Formulas

Momentum equals the mass of an object times its velocity: p (momentum) = mv

So an 20 kg object traveling at 100 m/s W:P(force) = 20 kg x 100 m/s west = 2000kg m/s west

If p = m x v, How would you find either mass or velocity (if you had force?) You would divide either into the force (P)

M = p/v or V = p/m

Inertia

Newton’s First Law of Motion proves that objects do not move or stop moving unless there are greater (unbalanced) forces acting upon them. This is what inertia is. Inertia is the object’s tendency to either keep moving or not moving at all. A force that changes this has to be strong enough to change an object’s inertia.

Can You Solve These Problems?

Look at the formulas and solve the following problems on speed, acceleration or momentum. Be sure to write down the formula first, plug in the numbers, and always write the ending units. You may want to underline or highlight the numbers in the problems.

Speed

1) The Jones family traveled north to New York. The family traveled a total of 480 miles in 12 hours. What was their average speed?

2) Myra is the school’s fastest runner. In her last race she ran for 10 seconds, and her average speed was 6 m/s. How far did she run?

Speed Problems1) 480 miles

12 hours = 40 miles/hr

2) Plug in the numbers you know:

_ ?___

6 m/s = 10 s (What does 10 go into 6 times?)

60 m

6 m/s = 10 s Does it work? Answer: 60 m

Acceleration Problems

3) Sam rode brother ‘s Big Wheel He started off traveling at 2 m/s. By the time Sam broke the toy, he had traveled for 4 s at 10 m/s. What was Sam’s rate of acceleration?

4) A train arrives at a station traveling at 10 miles per hour. 30 minutes ago it was traveling at 40 miles per hour. What was the train’s rate of acceleration?

Acceleration Problems

3) 10 m/s – 2 m/s 8 m/s

4 s = 4 s = 2 m/s/s

( or 2 m/s2)

4) Plug in what you know: 10 mph – 40 mph -30 mph

30 minutes = 30 minutes =

-1/m/hr every minute

Acceleration Problem

5) An airplane’s rate of acceleration is 50 m/s2. The starting speed was 100 m/s. After a while the plane was traveling at 200 m/s. How long did it take the plane to accelerate?

Plug in What You Know 200 m/s – 100 m/s

50 m/s2 = ?

Solve the first line:

100 m/s

50 m/s2 = ?

What goes into 100 50 times? 2!

100 m/s

50 m/s2 = 2 s Does it work?

Momentum Problems

6) An object with a mass of 50 kg is traveling at 14 m/s east. What is the force of this object?

7) An object thrown from a bridge has a force of 500g/m/s down. It has a mass of 125 g. What is the velocity of this object?

Plug It In!

6) P = m x v, so p = 50 kg x 14 m/s east

p = 700 kg/m every second east

7) 500 g/m per s down = 125 g x ? How many times does 125 go into 500? 4!

500 g/m per s down = 125 g x 4 m/s down Does it work?

Inertia

Inertia is a resistance to a change in motion. If an object is at rest, that is the inertia that has to be overcome. If an object is in motion, that is its inertia that has to be overcome.

Newton’s 1st Law deals with moving and nonmoving objects that require greater force – overcoming inertia!