Motion in One Motion in One DimensionDimension

Velocity and Velocity and AccelerationAcceleration

Describe the motion of the Describe the motion of the buggy.buggy.

This is a key term, one that you need to be sure to master in order to fully understand physics!

How does the motion of these 2 How does the motion of these 2 buggies compare?buggies compare?

What terms do we need to use?What terms do we need to use?

Is there a rate involved with their motion?Is there a rate involved with their motion?

DisplacementDisplacementA change in A change in position (position (X)X)

Distance (d)Distance (d)How far an object How far an object travelstravels

Positive Displacement (s)Positive Displacement (s)Moving in the Moving in the positive direction positive direction as determined by as determined by your frame of your frame of referencereference

Negative Displacement (-s)Negative Displacement (-s)Moving in the Moving in the negative direction negative direction as established by as established by your frame of your frame of referencereference

SpeedSpeed

Distance traveled per unit of timeDistance traveled per unit of time

V=d/tV=d/t

Units: m/sUnits: m/s

Scalar quantityScalar quantity (size only) (size only)

VelocityVelocity

Displacement an object experiences per Displacement an object experiences per unit of timeunit of time

V=s/V=s/tt

Units: m/s (with a direction)Units: m/s (with a direction)

Vector quantityVector quantity (size and direction) (size and direction)

Sample #1Sample #1

Heather and Matthew take 34 Heather and Matthew take 34 minutes to walk eastward along a minutes to walk eastward along a straight road to a store 2.0 km away. straight road to a store 2.0 km away. What is their average velocity in What is their average velocity in m/s?m/s?

0.98 m/s eastward0.98 m/s eastward

Sample #2Sample #2

Simpson drives his car with an Simpson drives his car with an average velocity of 24 m/s toward average velocity of 24 m/s toward the east. How long will it take him to the east. How long will it take him to drive 560 km on a perfectly straight drive 560 km on a perfectly straight highway?highway?

6.5 hours6.5 hours

Sample #3Sample #3

Eugeneville is 75.0 km due south of Eugeneville is 75.0 km due south of Salemtown. If Joe rides from Salemtown. If Joe rides from Salemtown to Eugeneville on his bike Salemtown to Eugeneville on his bike in 6.00 hours, what is his average in 6.00 hours, what is his average velocity in m/s?velocity in m/s?

3.47 m/s3.47 m/s

Sample #4Sample #4A bus traveled south along a straight A bus traveled south along a straight path for 3.2 hours with an average path for 3.2 hours with an average velocity of 88 km/h, stopped for 20.0 velocity of 88 km/h, stopped for 20.0 min, then traveled south for 2.8 min, then traveled south for 2.8 hours with an average velocity of 75 hours with an average velocity of 75 km/h. What is the average velocity km/h. What is the average velocity for the total trip? What is the for the total trip? What is the displacement for the total trip?displacement for the total trip?78 km/h south, 490 km south78 km/h south, 490 km south

How does the motion of the battery How does the motion of the battery car and buggy compare?car and buggy compare?

What terms do we need to use?What terms do we need to use?

Is there a rate involved with their motion?Is there a rate involved with their motion?

AccelerationAcceleration

Change in velocity per unit of timeChange in velocity per unit of time

a= a= v/v/tt

Units: m/sUnits: m/s22

Vector quantity (size and direction)Vector quantity (size and direction)

Sample #5Sample #5

When the shuttle bus comes to a When the shuttle bus comes to a sudden stop to avoid hitting a dog, it sudden stop to avoid hitting a dog, it slows from 9.00 m/s to 0.00 m/s in slows from 9.00 m/s to 0.00 m/s in 1.50 s. What is the average 1.50 s. What is the average acceleration of the bus?acceleration of the bus?

-6.00 m/s-6.00 m/s22

Sample #6Sample #6

With an average acceleration of -0.50 With an average acceleration of -0.50 m/sm/s22, how long will it take a cyclist to , how long will it take a cyclist to bring a bicycle with an initial velocity bring a bicycle with an initial velocity of +13.5 m/s to a complete stop?of +13.5 m/s to a complete stop?

27 s27 s

Is constant acceleration possible?Is constant acceleration possible?

Uniform AccelerationUniform Acceleration

s = ½ (Vs = ½ (Vii + V + Vff))tt No info on: aNo info on: a

Vf = VVf = Vii + a + att No info on: sNo info on: s

s = Vs = Viit + 1/2at + 1/2att22 No info on: VNo info on: Vff

VVff22 = V = Vii

22 + 2as + 2as No info on: No info on: tt

Note card Needed!

ViVi aa MotionMotion

++ ++ Speeding upSpeeding up

-- -- Speeding upSpeeding up

++ -- Slowing downSlowing down

-- ++ Slowing downSlowing down

- or +- or + 00Constant Constant velocityvelocity

00 - or + - or + Speeding up Speeding up from restfrom rest

00 00Remaining at Remaining at

restrest

Sample #7Sample #7

A car accelerates uniformly from rest A car accelerates uniformly from rest to a speed of 23.7 km/h in 6.5 s. Find to a speed of 23.7 km/h in 6.5 s. Find the distance the car travels during the distance the car travels during this time.this time.

21 m21 m

Sample #8Sample #8When Maggie applies When Maggie applies the brakes of her car, the brakes of her car, the car slows the car slows uniformly from 15.00 uniformly from 15.00 m/s to 0.00 m/s in m/s to 0.00 m/s in 2.50 s. How many 2.50 s. How many meters before a stop meters before a stop sign must she apply sign must she apply her brakes in order to her brakes in order to stop at the light?stop at the light?

18.8 m18.8 m

Sample #9Sample #9

A car with an initial speed of 23.7 A car with an initial speed of 23.7 km/h accelerates at a uniform rate of km/h accelerates at a uniform rate of 0.92 m/s0.92 m/s22 for 3.6 s. Find the final for 3.6 s. Find the final speed and the displacement of the speed and the displacement of the car during this time.car during this time.

36 km/h (9.9 m/s), +0.030 km36 km/h (9.9 m/s), +0.030 km

Sample #10Sample #10A driver of a car traveling at -15 m/s A driver of a car traveling at -15 m/s applies the brakes, causing a uniform applies the brakes, causing a uniform acceleration of +2.0 m/sacceleration of +2.0 m/s22. If the . If the brakes are applied for 2.5 s, what is brakes are applied for 2.5 s, what is the velocity of the car at the end of the velocity of the car at the end of the breaking period? How far has the the breaking period? How far has the car moved during the breaking car moved during the breaking period?period?-10. m/s, 32 m-10. m/s, 32 m

Sample #11Sample #11A baby sitter A baby sitter pushing a stroller pushing a stroller starts from rest starts from rest and accelerates at and accelerates at a rate of 0.500 a rate of 0.500 m/sm/s22. What is the . What is the velocity of the velocity of the stroller after it has stroller after it has traveled 4.75 m?traveled 4.75 m?

+2.18 m/s+2.18 m/s

Sample #12Sample #12Find the velocity Find the velocity after the stroller in after the stroller in #11 has traveled #11 has traveled 6.32 m.6.32 m.

+2.51 m/s+2.51 m/s

Sample #13Sample #13An aircraft has a liftoff speed of 120 An aircraft has a liftoff speed of 120 km/h. What minimum constant km/h. What minimum constant acceleration does this require if the acceleration does this require if the aircraft is to airborne after a take-off run aircraft is to airborne after a take-off run of 240 m?of 240 m?

+2.3 m/s2+2.3 m/s2

How long does it take the aircraft to How long does it take the aircraft to become airborne?become airborne?

14 s14 s

Let’s compare 5 cars!Let’s compare 5 cars!

Your goal is to establish a finish line that all 5 all 5 cars can cross cars can cross simultaneouslysimultaneously. They do not have to start at the same position. They should be powered by battery, rev motion or using a ramp set at a 45 degree angle. They do all need to cross your tape finish line at the same time. You should show all calculations prior to attempting experimental validation!