MotionMotion11.2 Speed and Velocity11.2 Speed and Velocity

Chapter 11Chapter 11

What are we going to learn?What are we going to learn?► Identify types of speed Identify types of speed ►Calculate the speed of an objectCalculate the speed of an object

SpeedSpeed►The The ratioratio of the of the distancedistance an object moves an object moves

to the to the amount of timeamount of time the object moves the object moves►2 types: 2 types: averageaverage and and instantaneousinstantaneous

Average vs. Instantaneous Average vs. Instantaneous SpeedSpeed

►http://www.physicsclassroom.com/http://www.physicsclassroom.com/mmedia/kinema/trip.cfmmmedia/kinema/trip.cfm

Average Speed Average Speed ►Total distance Total distance traveled traveled divided bydivided by the the

timetime it takes to travel that distance it takes to travel that distance ►Average speedAverage speed is computed for the is computed for the entire entire

durationduration of a trip of a trip

►FormulaFormula for average speed is: for average speed is:Total distance

Total timeAverage speed = or, d

t

Instantaneous Speed Instantaneous Speed ►Rate Rate at which an object is at which an object is movingmoving at a at a

given given moment in time moment in time ► Instantaneous speed is Instantaneous speed is measuredmeasured at a at a

particular instant particular instant

Speed GraphsSpeed Graphs►The The slopeslope of a line on a of a line on a distance-time distance-time

graphgraph is is speed speed

Velocity Velocity ►Description of both Description of both speed speed

and and directiondirection of motion of motion►VelocityVelocity is a is a vectorvector

►A A changechange in in velocityvelocity can be the can be the result ofresult of a a change in change in speedspeed, a change in, a change in direction direction, or , or bothboth

►Two or moreTwo or more velocities velocities addadd by by vector vector additionaddition

►A A boatboat on a river heads on a river heads straight acrossstraight across the the river. The river. The currentcurrent is moving is moving parallelparallel to the to the river banks, so the river banks, so the boatboat does does notnot land on the land on the bank bank directly acrossdirectly across from the starting location. from the starting location.

►The The resulting motionresulting motion of the boat is the of the boat is the vectorvector sumsum of the of the boat velocityboat velocity plus the plus the river river velocityvelocity. .

►The boat starts at Point The boat starts at Point A A and heads and heads towardstowards Point Point B B but but reachesreaches the opposite the opposite bankbank of the of the river at Point river at Point CC. .

►The The timetime required for the boat to cross required for the boat to cross the river from one side to the other side the river from one side to the other side dependsdepends on the on the boat velocityboat velocity and the and the width of the riverwidth of the river

► If the If the boat velocityboat velocity is is 4 m/s4 m/s and the and the riverriver velocityvelocity is is 3 m/s3 m/s, the , the resultant velocityresultant velocity could be determined to be could be determined to be 5 m/s5 m/s using using the Pythagorean Theorem (the Pythagorean Theorem (aa22 + b + b22 = c = c22))

►The boat velocity is The boat velocity is aa, river , river velocity is velocity is bb, then the resultant velocity is , then the resultant velocity is cc

►a = a = 44 m/s and b = m/s and b = 33 m/s m/s►aa22 + b + b22 = c = c22

4422 + 3 + 322 = c = c22

1616 + + 99 = c = c22

√ √¯̄ 2525 = c = c 55 = c = c►The resultant velocity is 5 m/sThe resultant velocity is 5 m/s

►The time (t) required for the boat to cross The time (t) required for the boat to cross a 60-meter wide river (d) would be a 60-meter wide river (d) would be dependent upon the boat velocity of 4 dependent upon the boat velocity of 4 m/s (v)m/s (v)

► If If d = v • td = v • t then then t = d / vt = d / v so so t = d / vt = d / v = (60 m) / (4 m/s) = = (60 m) / (4 m/s) = 15 15

secondsseconds► It would require 15 seconds to cross the It would require 15 seconds to cross the

60-meter wide river60-meter wide river

►The teacher walks 4 meters East, 2 The teacher walks 4 meters East, 2 meters South, 4 meters West, and finally meters South, 4 meters West, and finally 2 meters North. The entire motion lasted 2 meters North. The entire motion lasted for 24 seconds. for 24 seconds.

►Determine the average speed and the Determine the average speed and the average velocity.average velocity.

*

Average SpeedAverage Speed►To determine average speed:To determine average speed: d = d = 1212 meters meters t = t = 2424 seconds seconds average speed = d/taverage speed = d/t = = 12 m/ 24 12 m/ 24 = = 0.500.50 m/s m/s

Average VelocityAverage Velocity►Average velocity is displacement (speed Average velocity is displacement (speed

with change in direction)/time with change in direction)/time v = d / tv = d / t ►The displacement is The displacement is 00 meters meters ►Average velocity = Average velocity = 0 m/24 s0 m/24 s►Average velocity = Average velocity = 0 m/s0 m/s

► The skier moves from A to B to C to D. The skier moves from A to B to C to D. ►Determine the average speed and average Determine the average speed and average

velocity of the skier during these 3 minutes.velocity of the skier during these 3 minutes.

Remember: Add up the distances for speedRemember: Add up the distances for speed Add up the displacements for velocity Add up the displacements for velocity

►A football coach, Seymour, is pacing back A football coach, Seymour, is pacing back and forth along the sidelines from and forth along the sidelines from position A to B to C to D. position A to B to C to D.

►What is the coach's average speed and What is the coach's average speed and average velocity? average velocity?

Questions...Questions...►Define speed.Define speed.The ratio of the distance an object moves The ratio of the distance an object moves

to the amount of time the object moves.to the amount of time the object moves.

►The SI units for speed are The SI units for speed are meters per meters per second (m/s)second (m/s)..

►How is instantaneous speed different How is instantaneous speed different from average speed? from average speed?

Average speed: speed is calculated for the Average speed: speed is calculated for the entire duration of a tripentire duration of a trip

Instantaneous speed: speed that is Instantaneous speed: speed that is measured at a particular instantmeasured at a particular instant

►The equation used for calculating average The equation used for calculating average speed is speed is total distance divided by total total distance divided by total time (d/t)time (d/t)..

►True or false? True or false? You can determine how fast you were You can determine how fast you were

going at the midpoint of a trip by going at the midpoint of a trip by calculating averagecalculating averagespeed for the entire trip. speed for the entire trip.

False, the midpoint speed is an False, the midpoint speed is an instantaneous speed.instantaneous speed.

►A student walked 1.5 km in 25 minutes, A student walked 1.5 km in 25 minutes, and then, realizing he was late, ran the and then, realizing he was late, ran the remaining 0.5 km in 5 minutes. Calculate remaining 0.5 km in 5 minutes. Calculate his averagehis averagespeed on the way to school.speed on the way to school.

Average speed = Average speed = (1.5 km + 0.5 km)(1.5 km + 0.5 km) (25 min + 5 min)(25 min + 5 min) = 0.067 km/min= 0.067 km/min

►What type of speed does an automobile’s What type of speed does an automobile’s speedometer display? speedometer display?

►What type of speed does an automobile’s What type of speed does an automobile’s speedometer display? speedometer display?

Instantaneous speedInstantaneous speed

►The slope of a line on a distance-time The slope of a line on a distance-time graph represents graph represents speedspeed..

►How do speed and velocity differ? How do speed and velocity differ? Speed: distance and time are factorsSpeed: distance and time are factorsVelocity: distance, time and Velocity: distance, time and directiondirection are are

factorsfactors

►Circle the letter of each sentence that Circle the letter of each sentence that describes a change in velocity.describes a change in velocity.

a.a. A moving object gains speed. A moving object gains speed.b. A moving object changes direction.b. A moving object changes direction.c.c. A moving object moves in a straight A moving object moves in a straight

line at a constant speed.line at a constant speed.d. A moving object slows down.d. A moving object slows down.

►True or false? True or false? If a car travels around a gentle curve on a If a car travels around a gentle curve on a

highway at 60 km/h, the velocity does not highway at 60 km/h, the velocity does not change. change.

False, it’s direction changes as it goes False, it’s direction changes as it goes around the curve.around the curve.

►How do velocities combine? How do velocities combine? Sum of vectors in magnitude and directionSum of vectors in magnitude and direction

►A river flows at a velocity of 3 km/h A river flows at a velocity of 3 km/h relative to the riverbank. A boat moves relative to the riverbank. A boat moves upstream at a velocity of 15 km/h relative upstream at a velocity of 15 km/h relative to the river. What is the velocity of the to the river. What is the velocity of the boat relative to the riverbank?boat relative to the riverbank?

a.a. 18 km/h downstream18 km/h downstream b. 15 km/h b. 15 km/h upstreamupstream

c.c. 12 km/h upstream12 km/h upstream d. 12 km/h d. 12 km/h downstreamdownstream

(Remember: 3 km/h downstream + 15 (Remember: 3 km/h downstream + 15 km/h upstream = 12 km/h upstream)km/h upstream = 12 km/h upstream)

►A person jogs 4.0 km in 32 min, then 2.0 A person jogs 4.0 km in 32 min, then 2.0 km in 22 min, and finally 1.0 km in 16 km in 22 min, and finally 1.0 km in 16 min. What is the jogger’s average speed min. What is the jogger’s average speed in km/min?in km/min?

0.1 km/min0.1 km/min(4.0 km + 2.0 km + 1.0 km)(4.0 km + 2.0 km + 1.0 km)(32 min + 22 min + 16 min)(32 min + 22 min + 16 min)= = 7.0 km7.0 km 70 min70 min= 0.1 km/min= 0.1 km/min

►A train travels 190 km in 3.0 hr, and then A train travels 190 km in 3.0 hr, and then 120 km in 2.0 hr. What is its average 120 km in 2.0 hr. What is its average speed?speed?

(190 km + 120 km)(190 km + 120 km) (3.0 hr + 2.0 hr)(3.0 hr + 2.0 hr)= = 310 km310 km 5.0 hr5.0 hr= 6.2 km/hr= 6.2 km/hr

►A car travels 85 km from point A to point A car travels 85 km from point A to point B, then 45 km from B to C. The total trip B, then 45 km from B to C. The total trip took 1.5 hr. What was the average speed took 1.5 hr. What was the average speed of the car?of the car?

(85 km + 45 km)(85 km + 45 km) 1.5 hr1.5 hr= 86.7 km/hr or 87 km/hr= 86.7 km/hr or 87 km/hr

►A bicyclist travels for 1.5 hr at an average A bicyclist travels for 1.5 hr at an average speed of 32 km/hr. How far does the speed of 32 km/hr. How far does the bicyclist travel in that time?bicyclist travel in that time?

Average speed = d/t (solve for d)Average speed = d/t (solve for d)32 km/hr = d/1.5hr32 km/hr = d/1.5hr32 km/hr x 1.5 hr = d32 km/hr x 1.5 hr = d48 km = d48 km = d

►Draw and label a line showing the slope Draw and label a line showing the slope of a constant high speed (A), constant low of a constant high speed (A), constant low speed (B), and varying speed (C) on the speed (B), and varying speed (C) on the graph below.graph below.

A

B

C

►Does a car’s speedometer show Does a car’s speedometer show instantaneous speed, average speed, or instantaneous speed, average speed, or velocity? Explain. velocity? Explain.

Instantaneous speed: it shows the speed at Instantaneous speed: it shows the speed at one instant in time not over a whole trip one instant in time not over a whole trip nor does it indicate directionnor does it indicate direction

►Describe an experiment you could Describe an experiment you could perform to determine the average speed perform to determine the average speed of a toy car rolling down an incline.of a toy car rolling down an incline.

Average speed calculations require Average speed calculations require distance and time. distance and time.

An experiment would involve timing the car An experiment would involve timing the car from a starting point to an end point and from a starting point to an end point and also measuring the distance between the also measuring the distance between the 2 points.2 points.

►A plane’s average speed between 2 cities A plane’s average speed between 2 cities is 600 km/h. If the trip takes 2.5 hours, is 600 km/h. If the trip takes 2.5 hours, how far does the plane fly?how far does the plane fly?

Average speed = d/tAverage speed = d/t600 km/h = d/2.5 h600 km/h = d/2.5 h600 km/h x 2.5 h = d600 km/h x 2.5 h = d1500 km = d1500 km = d