Motion

Motion is Relative Even things that appear to be at rest move. When we describe the motion of one object with respect to another, we say that the object is moving relative to the other object. A book that is at rest, relative to the table it lies on, is moving at about 30 kilometers per second relative to the sun. Although you may be at rest relative to Earth’s surface, you’re moving about 100,000 km/h relative to the sun. Unless stated otherwise, the speeds of things in our environment are measured relative to the surface of Earth.

Frame of Reference The position from which the motion is being observed. Your frame of reference affects the motion you perceive. Example: You are travelling 55 mph on the freeway and another car passes you. What is the other car’s speed relative to you? What is your speed relative to the other car? What is your speed relative to a person standing on the side of the road?

Scalar vs. Vector What is the difference between a scalar quantity and a vector quantity? Scalar – a measurement describing the magnitude (or value) only, no direction Ex: Mass, temperature, volume Vector – a measurement describing the magnitude and direction Ex: Velocity, acceleration, force

So how do we know an object is moving? An object is in motion if its position changes. The simplest kind of motion an object can experience is uniform motion in a straight line or linear motion.

What is the difference between distance and displacement? Distance: How far something travels - a scalar. Displacement: How far something travels in a given direction. That means displacement is a vector.

A skier travels from A to B then to C then to D. What distance does she travel? 420 m 180 + 140 + 100 = What is her displacement at D? 140 m right of A

AVERAGE SPEED If an object takes a time interval t to travel a distance d, then the average speed of the object is given by: S = d/t Units for speed: distance (d) is in meters (m) time (t) is in seconds (s) so, speed (S) is in meters/second (m/s) Speed is a scalar.

Why average speed? As the car moves, it often undergoes changes in speed. For example, during an average trip to school, there are many changes in speed. Rather than the speedometer maintaining a steady reading, the needle constantly moves up and down to reflect the stopping and starting and the accelerating and decelerating. The reading on the speedometer at any point in time would be the instantaneous speed.

VELOCITY Velocity is speed in a given direction, so velocity is a vector like displacement. That means the formula for velocity is the same as the formula for speed and the units are the same. V = d/t Example: If the speed of a skier in a previous slide could be 10 m/s. The skier’s velocity would be 10 m/s downhill.

Observe the animation of the three cars below Observe the animation of the three cars below. How would you describe the motion of the red car? the green car? the blue car? The rate at which velocity changes is ACCELERATION

Units: m/s2 ACCELERATION Acceleration is the rate of change of velocity. The change in velocity ΔV is the final velocity Vf minus the initial velocity Vi. Units: m/s2 Acceleration is also a vector, i.e. it has a direction.

STOP HERE

Motion Problems

SPEED If an object takes a time interval t to travel a distance d, then the speed of the object is given by: S = d/t Units for speed: distance (d) is in meters (m) time (t) is in seconds (s) so, speed (S) is in meters/second (m/s) Speed is a scalar.

VELOCITY Velocity is speed in a given direction, so velocity is a vector like displacement. That means the formula for velocity is the same as the formula for speed and the units are the same. V = d/t Average Speed or Average Velocity would be the total distance travelled divided by the total time.

Duncan Phillips AMCHS ‘07 Example 1: A runner makes one lap around a 200 m track in a time of 25 s. What is the runner's average speed? Givens: Formula: Answer: Work: Diagrams: d = 200 m t = 25 s 8 m/s S = d t Unknown: S = ? S = d t m s = 8 m/s Duncan Phillips AMCHS ‘07 ‘O6 State Gold Medal 1600 m

Example 2: According to the World Disk Federation, on April 8,2000 Jennifer Griffin threw a Frisbee for a distance of 138.56 m to capture the woman’s record. If the Frisbee was thrown horizontally with a speed of 13.0 m/s, how long did the Frisbee remain aloft? Givens: Formula: Answer:   Work: Diagrams: S = d t = 10.7 s S = 13.0 m/s d = 138.56 m t = ? S = d t 13.0 m/s = 138.56 m t t = 138.56 m = 10.658 s 13.0 m/s

Observe the animation of the three cars below Observe the animation of the three cars below. How would you describe the motion of the red car? the green car? the blue car? The rate at which velocity changes is ACCELERATION

Units: m/s2 ACCELERATION Acceleration is the rate of change of velocity. The change in velocity ΔV is the final velocity Vf minus the initial velocity Vi. Units: m/s2 Acceleration is also a vector, i.e. it has a direction.

A positive acceleration means an increase in velocity; a negative acceleration usually means a decrease in velocity (deceleration). Note that negative acceleration is in OPPOSITE direction of the velocity

Example 1: A truck’s speed increases uniformly from 5 m/s to 15 m/s in 20 seconds. Determine the acceleration. Givens: Formula: Answer:   Work: Unknown: a = Vf – Vi t Vi = 5 m/s Vf = 15 m/s t = 20 s a = 0.5 m/s2 a = (15 m/s – 5 m/s) 20 s a = ? A = 10 m/s = 0.5 m/s2 20 s

The acceleration equation can also be written as follows: This version of the formula is easier to use if you are trying to find vf, vi, or time.

Example 2: A bus begins accelerating from a stop sign at 3 m/s2 Example 2: A bus begins accelerating from a stop sign at 3 m/s2. After 20 seconds, what is the buses’ new speed? Givens: Formula: Answer:   Unknown: Vf = 60 m/s Vi = 0 m/s a = 3 m/s2 t = 20 sec Vf = 0 m/s + (3 m/s2)(20 sec) Vf =?

DISPLACEMENT Distance or displacement can be calculated using the following equation: d = vit + ½ at2 This formula could also be used to find the acceleration if d, vi and time are known.

Example 3: A truck initially at rest accelerates at 3 m/s2 to 20 m/s in 8 seconds. How far has the truck travelled in that time? Givens: Formula: Answer:   Work: Unknown: d = vit + ½ at2 Vi = 0 m/s Vf = 20 m/s a = 3 m/s2 t = 8 s d = 96 m d = (0)(8 s) + ½ (3 m/s2)(8 s2) d = ?