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Motion Notes Motion happens when an object changes its position. Reference points are used to determine if something is moving or not. A reference point is a place or object used for comparison to determine if an object is in motion. If there is a change in distance between the reference point and the object, then the object is in motion. Using the man in the car as our reference point, the dog is not moving. Using the white car as our reference point, the dog is moving.

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How do you know the mail truck has moved? (What did you use as a reference point? ______________________)

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Distance – is how far something has moved. In order to find out what sort of motion takes place, distance needs to be measured. The SI unit of length or distance is meters (m). Displacement/Position – is the distance and direction of an object’s change in position from the starting point. In the picture on the right, label letters A and B as being either displacement or distance. A = __________________________ B = __________________________

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How far has this runner been displaced from the starting line? (What’s the position from the starting line?) ___________________ What is the total distance this runner has ran? ___________________

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Example: A cyclist traveled 100 miles in 10 hours. What was his speed? Variables: d = t = S = Formula: Solve: Speed – is how far something travels in a given amount of time or the distance traveled per amount of time. The variable for speed is S The SI unit for speed is m/s (meters per second)

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Much of the time, the speeds you experience are not constant. Think about riding a bicycle for a distance of 5 km. As you start out, your speed increases from 0 km/h to, say, 20 km/h. You slow down to 10 km/h as you pedal up a steep hill and speed up to 30 km/h going down the other side of the hill. You stop for a red light, speed up again, and move at a constant speed for a while. As you near the end of the trip, you would slow down and then stop. Checking your watch, you find that the trip took 15 min, or one-quarter of an hour. How would you express your speed on such a trip? Would you use your fastest speed, your slowest speed, or some speed between the two?

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CAREFUL! Distance is 0 miles because “stopped for lunch”. Average speed – is the total distance traveled over the total amount of time. Formula: Average speed = Total distance/Total time or S avg = d total /t total Example: A person walks 4 miles in 2 hours then stops for an hour for lunch. After lunch they walk 8 miles in 3 hours. Calculate the person’s average speed. Variables: Formula: Solve: DISTANCETIME 4 miles2 hours 0 miles1 hour 8 miles3 hours 12 total mi6 total hrs

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Instantaneous Speed Suppose you watch a car’s speedometer go from 0 km/h to 60 km/h. A speedometer shows how fast a car is going at one point in time or at one instant. The speed shown on a speedometer is the instantaneous speed. Instantaneous speed – is the speed at a given point in time.

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Time is always an independent variable (x-axis). Graphing Motion as CONSTANT SPEED Graphing Conventions:The dependent variable is always on the y-axis. DRY The independent variable is always on the x-axis. MIX Examples of units of Speed: km/s, km/h, m/s, mi/h, cm/yr … Faster constant speed Slower constant speed Start, stop, start

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Distance or Position vs. Time Graph Slope = speed (Slope is rise/run) (Speed is distance/time) The slope (or speed) of a flat line is zero or no speed. The object is at rest (stopped). Graph 1

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Graph 2: A car travels at a constant speed of 6 m/s (S = 30 m/5 s). The graph of constant speed is a slanted straight line. Notice that the speed is the same at every point on the graph. How far does the car go in 4 seconds? Variables: S = 6 m/s;t = 4 s;d = ? Formula: Solution:

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Graph 3: The same car travels at a constant speed of 1.0 m/s (S = 10 m/10 s). The graph of constant speed is a slanted straight line. Notice that the slope of the line is more gradual and every point on the graph has the same speed. How far does the car go in 4 seconds at its new speed? Variables: S = 1.0 m/s;t = 4 s;d = ? Formula: Solution:

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Velocity Escalators are found in shopping malls and airports. The up and down escalators move their passengers at a constant speed, but in opposite directions. The speeds of the passengers are the same, but their velocities are different because the passengers are moving in different directions.

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Velocity – includes the speed of an object and the direction of its motion. VELOCITY = Distance/time AND direction Example: 5,000 m/s south Example: A car moving northward at 60 km/hr passes a car moving southward at 60 km/hr. Both have the same speed but each has a different velocity. *** Velocity is calculated like speed but a direction is given. The speed of this car is constant, but its velocity is not constant because the direction of motion is always changing.

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Acceleration Acceleration – is the rate of change of velocity. This includes changes in speed, direction, or both. If an object changes velocity, it is accelerating. An object that slows, speeds up, turns, or stops, is accelerating.

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PRACTICE PROBLEMS: 1.What would be the velocity of a storm moving west, if it traveled at 108 km in 2 hours? 2.What is your average velocity if you travel east for a distance of 300 miles in 2.5 hours? 3.A storm is moving east at a velocity of 60 km/hr. If the storm is 140 km west of our location, how many hours will it take for the storm to reach us?

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WHICH OF THE FOLLOWING SHOWS A CHANGE IN ACCELERATION??? 1.The red Mustang maintains its speed between points A and B. 2.Between points B and C the Mustang increases speed on the long stretch. 3.Between C and D the car changes direction heading south and slows in speed. 4.There was a roadside park at D so the driver stopped and rested. 5.There were store windows between D and E and the driver slowed the car’s speed to a creep.

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Acceleration Example: A plane starts at rest and ends up going 200 m/s in 10 seconds. Calculate the acceleration. Step 1: Variables: V i = starting speed = 0 m/s (“starts at rest”); V f = ending speed = 200 m/s, ∆t =10s

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Deceleration (Negative Acceleration) Example: A race car starts at 400 m/s and then stops in 20 seconds. Calculate the car’s acceleration. Step 1: Variables: V i =400 m/s; V f = 0 m/s; ∆t = 20 m/s *** Take note of the negative sign. This represents deceleration or slowing down.

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Gravity Acceleration due to gravity is always a constant 9.8 m/s 2.

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PRACTICE PROBLEMS 1.A biker starts to move and goes from 0 m/s to 25 m/s in 10 s. What is the acceleration? Variables:

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2.A biker goes from a speed of 20 m/s to 8 m/s in 6 s. What is the acceleration? Variables:

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3.A driver starts his parked car and attains an acceleration of 3 m/s 2 in 5 seconds. What is the final speed? Variables:

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A slow-moving object is easier to stop than a fast-moving object. Increasing either the speed or mass of an object makes it harder to stop. A moving object has a property called momentum that is related to how much force is needed to change its motion. The momentum of an object is the product of its mass and velocity. Momentum is given the symbol p and can be calculated with this equation: p = m x v Momentum = mass x velocity The unit for momentum is kg m/s. Note that momentum has a direction because velocity as a direction.

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In the picture at right, the two trucks might have the same velocity, but the bigger truck has more momentum because of its greater mass. An archer’s arrow can have a large momentum because of its high velocity, even though its mass is small. A walking elephant may have a low velocity, but because of its large mass, it has a large momentum.

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Law of Conservation of Momentum The momentum of an object doesn’t change unless its mass, velocity, or both change. Momentum, however, can be transferred from one object to another.

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Momentum is transferred in collisions. Consider a game of pool. Before the game starts, all the balls are motionless. The total momentum of the balls is, therefore, zero. What happens when the cue ball hits the group of balls that are motionless? The cue ball slows down and the rest of the balls begin to move. The total momentum of all the balls just before and after the collision would be the same. The momentum the group of balls gained is equal to the momentum that the cue ball lost. The total momentum is conserved—it isn’t created or lost.

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The results of a collision depend on the momentum of each object. When a puck hits another puck from behind, its gives the second puck momentum in the same direction. If the pucks are speeding toward each other with the same speed, the total momentum is zero. (How will they move after they collide?)

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