Chapter 2 Motion and Speed

Sec. 1 Describing Motion Motion occurs when an object changes position. You don’t need to see it move to know that motion has happened. You just need a reference point

Distance and Displacement Distance—how far an object moved The SI unit for distance is the meter,m Displacement—the distance and direction of an object’s change in position from the starting point.

Distance Vs Displacement Animation

Distance can be longer than Displacement Displacement cannot be longer than Distance Distance and Displacement can be the same.

Speed Rate—any change over time Speed—the distance an object travels per unit of time. Speed = distance s = d time t Ex. You ran 2 km in 10 min, what is your speed? s = 2 km / 10 min s = 0.2 km/min

Average & Instantaneous Speed Average speed—total distance traveled divided by total travel time. Used when speed is changing Instantaneous speed—the speed at a given point in time. Ex. Speedometer

Velocity Speed describes only how fast something is moving. Velocity—includes the speed of an object AND the direction of its motion Ex: 40 mi/hr North or 5 m/s up

Change in Velocity Velocity can change in 2 ways Change in speed Change in direction Or Both Ex: a race car has a constant speed of 100km/hr around an oval track. Speed is constant, but velocity changes

Graphing Motion On a distance vs. time graph, time goes on the x-axis and distance goes on the y-axis. The slope (steepness) of the line represents the speed of the object.  Distance Speed Time↓

Positive Speed Positive Speed: Moving away from the origin or reference point Graph has a positive (upward) slope

Constant, Positive Speed Straight Line Speed isn’t changing

Fast vs. Slow Positive Speed Slow: has a shallow, gradual slope Fast: has a steep slope

Changing, Positive Speed Graph has a curve The slope is changing, so speed is changing Speeding Up Slowing Down

Constant, Negative speed Negative Speed: Moving toward the origin or reference point Graph has a negative (downward) slope Constant, Negative speed

Fast vs. Slow Negative Speed Fast: steep, downward slope Slow: shallow, gradual downward slope

Changing, Negative Speed

Not Moving (0 speed) A horizontal line (zero slope) indicates no motion (or no change from the origin)

Which one is the fastest? Which isn’t moving?

Rearranging the speed equation The original speed equation is s=d/t This can be rearranged to solve for d or t. s = d t d = s x t (how far?) t = d (how long?) s

#1 How long will it take a bike rider to travel 450 meters at a constant speed of 2 m/s?

#2 If a car traveled 2500 m in 20 minutes, what is the average speed of the car?

#3 If a bug travels for 50 seconds at 4 meters per second, how far does it travel?

Acceleration Acceleration: Change in velocity over time When something speeds up, it has a positive acceleration When something slows down, it has a negative acceleration Units for acceleration have one distance unit and 2 time units Example Units: m/s/s or m/s2, mi/hr/min

Changing Direction A change in velocity can be either a change in speed or a change in direction. Any time an object changes direction, its velocity changes and it is accelerating.

Calculating Acceleration Acceleration Equation: acceleration = change in velocity time Change in velocity = final velocity (vf) – initial velocity(vi) We can write the acceleration equation as a = (vf – vi) t (vf -vi) a t

Graphing Acceleration On a Velocity vs Time Graph, the slope of the line is the acceleration Positive acceleration has an upward slope Positive Acceleration (speeding up) + acceleration

Negative Acceleration (Slowing Down) Negative acceleration has a downward slope - acceleration

Zero Acceleration When an object has a constant velocity, it has 0 acceleration, so the graph is a horizontal line. velocity 0 acceleration time

An Object Changing Acceleration

Acceleration Example #1 An airplane starts at rest and speeds up to 80m/s at the end of the runway in 20 s. What is its acceleration? a = (vf – vi) = (80 m/s – 0 m/s) t 20 s = 4 m/s2 The airplane is speeding up, so the acceleration is positive.

Acceleration Example #2 A skateboarder is moving at 3 m/s and comes to a stop in 2 s. What is the acceleration? a = (vf – vi) = (0 m/s – 3 m/s) = -1.5 m/s2 t 2 s The skateboarder slowed down, so the acceleration is negative. Note: words like at rest and stop mean velocity = 0.