Physics 30S

Kinematics – Part A

What is Kinematics?

• Kinematics describes the motion of objects.• How do things move?• What is displacement, velocity and

acceleration?

Outcomes• S4P-1-1 Derive the special equations for constant

acceleration. Include:

• S4P-1-2 Solve problems for objects moving in a straight line with a constant acceleration. Include:

• S4P-1-3 Solve relative motion problems for constant velocities using vectors.

The Big 4

Derivation of Big 4

• See Derivation of Big 4.pdf• Derivation Notes

What are the Big Ideas of the Derivation?

Problem Solving

• Step 1: Identify what is given• Step 2: Identify what is asked• Step 3: Select an equation• Step 4: Solve• Step 5: Sig Figs!

Question 1

An airplane accelerates from rest down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff.

a = +3.2 m/s2

t = 32.8 svi = 0 m/s

Find d = ??

d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)2

d = 1720 m

Question 2A car starts from rest and accelerates uniformly

over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.

d = 110 mt = 5.21 svi = 0 m/s

Find:a = ??

110 m = (0 m/s)*(5.21 s)+ 0.5*(a)*(5.21 s)2

110 m = (13.57 s2)*aa = (110 m)/(13.57 s2)a = 8.10 m/s2

a = 8.1 m/s2

Question 3A race car accelerates uniformly from 18.5 m/s to

46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled.

vi = 18.5 m/s

vf = 46.1 m/s

t = 2.47 s

Find:d = ?? a = ??

46.1 m/s = 18.5 m/s + (a)(2.47 s)a = 11.2 m/s2

d = (18.5 m/s+ 46.1 m/s)(0.5)(2.47 s)d = 79.8 m

2 Part Questions

• Are there other ways to solve?– Yes, but...

• Don’t use calculated values for 2nd part questions wherever possible!– Calculation errors can carry over into later

questions– Can run into rounding problems if you use

significant figure value

Question 4

A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of the bike.

vi = 0 m/s

vf = 7.10 m/s

d = 35.4 m

Find:a = ??

(7.10 m/s2)2 = (0 m/s)2 + 2*(a)*(35.4 m)a = 0.712 m/s2

Homework

• Big 4 Problems Handout– Leave out #3

Acceleration due to Gravity• Acceleration due to gravity on earth: a = -9.8

m/s2

– Use this value in calculations as acceleration• Acceleration due to gravity is different on

other planets, so watch out for location!– More to come later

Question 1Acceleration due to gravity: a = -9.8 m/s2

Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far will he fall?

a = -9.8 m/s2

t = 2.6 svi = 0 m/s

Find:d = ?? vf = ??

d = (0 m/s)*(2.6 s)+ 0.5*(-9.8 m/s2)*(2.6 s)2

d = 33 m

vf = vi + a*tvf = 0 + (-9.8 m/s2)*(2.6 s)vf = -25.5 m/s (- indicates direction)

Question 2

A kangaroo is capable of jumping to a height of 2.62 m. Determine the takeoff speed of the kangaroo.

a = -9.8 m/s2

vf = 0 m/s

d = 2.62 m

Find:vi = ??

(0 m/s)2 = vi2 + 2*(-9.8 m/s2)*(2.62 m)

vi = 7.17 m/s

Question 3

A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s2. Determine the time for the feather to fall to the surface of the moon.

vi = 0 m/s

d = -1.40 ma = -1.67 m/s2

Find:t = ??

d = (0 m/s)*(t)+ 0.5*(-1.67 m/s2)*(t)2

t = 1.29 s

Homework

• Physics, Concepts and Conceptions– P.64 # 1 ,2, 3, – P.70 #50, 54, 55, 69

• Big 4 Handout – #3

Interval Questions

• 2 Big 4 questions rolled into 1• Must be worked out in intervals– Different accelerations during different phases of

the questions• What happened during the first acceleration?

What happened during the second acceleration?

• Very important – Label your intervals clearly!

Question 1Otto Emissions is driving his car at 25.0 m/s. Otto accelerates at 2.0 m/s2

for 5.00 seconds. Otto then maintains a constant velocity for 10.0 more seconds. Calculate the total distance traveled during the entire 15 seconds.

Given:Interval 1vi = 25.0 m/s

t = 5.00 sa = 2.0 m/s2

Find: d = ??

Interval 2t = 10.0 sa = 0.0 m/s2

Find: d = ??

d = 500. m

Question 2Vera Side is speeding down the interstate at 45.0 m/s when she

observes a pileup in the middle of the road. When she first sees the accident, she is 80.0 m from the pileup. She slows down at a rate of -10.0 m/s2. Assuming it will take her 0.0500 s to hit the brakes, determine the distance which Vera Side would travel prior to reaching a complete stop (if she did not collide with the pileup). Will Vera hit the cars in the pileup?

Since the accident pileup is less than 103 m from Vera, she will indeed hit the pileup before completely stopping (unless she veers aside).

Total distance: 104 m

Homework

• Interval Questions handout

2 Object Problems

• 2 different objects, each with its own velocity and acceleration

• Usually there is one quantity which is shared by both objects– Same distance to travel, must catch up with each

other, etc.• Keep clear which quantities belong to which

object!• Draw a picture!

Question 1

Fred and his friend Barney are at opposite ends of a 1.0 km long drag strip. Fred accelerates from rest toward Barney at 2.0 m/s2. Barney travels toward Fred at a constant speed of 10 m/s. How much time elapses before Fred and Barney collide?

t = 27 s

Question 2

Jack, who is running at 6.0 m/s to catch a bus, sees it start to move when he is 20.0 m away from it. If the bus accelerates at 1.0 m/s2, will Jack overtake it? If so, how long will it take him?

Jack misses the bus!

Homework

• Physics, Concepts and Conceptions• Pg.75 #66, 67, 68

Relative Motion

• Relative motion occurs when an object appears to have one motion to one observer and a different motion to a second observer.

• Observers are moving relative to each other• Examples:– Boat crossing a river– Airplane flying through the air– 2 cars on the highway

Relative Motion – What to Do?

• Velocity of the object relative to the ground is equal to the velocity of the object relative to the medium plus the vector sum of the velocity of the medium relative to the ground.

• AKA: Vector sums are back!!!!

Question 1

A sports car is travelling east on Highway #1 at 140 km/h and a semi is travelling west on the same highway at 110 km/h.

a) If you were in the sports car, what is the apparent velocity of the truck?

250 km/h, Wb) If you were the truck driver, what is the

apparent velocity of the sports car?250 km/h, E

Question 2A sports car is travelling east on Highway #1 at 140 km/h

and a semi is travelling east on the same highway at 110 km/h.

a) If you were in the sports car, what is the apparent velocity of the truck?

30 km/h, Wb) If you were the truck driver, what is the apparent

velocity of the sports car?30 km/h, Ec) If you are a police office parked at the side of the road,

what is the apparent velocity of both vehicles?Sports car: 140 km/h, ESemi: 110 km/h, E

What about Kinematics?

• Kinematics equations (and classical mechanics in general) are valid for non-inertial reference frames

• Can’t use if you’re accelerating and observing motion

Question 3

A boat is crossing a river at 2.00 m/s, N relative to the water. The river has a current of 2.00 m/s, E relative to the shore. What is the velocity of the boat relative to the shore?

Homework

• Physics, Concepts and Conceptions• P. 116 #35, 36,

Review• Create a foldable highlighting each of the Big 4 Equations!

Big 4 Equation: Big 4 Equation:

Big 4 Equation: Big 4 Equation:

Variables Used:

Variables Not Present:

Sample Problem & Solution: Sample Problem & Solution: Variables Used:

Variables Not Present:

Variables Used:

Variables Not Present:

Sample Problem & Solution: Sample Problem & Solution: Variables Used:

Variables Not Present:

Outside

Inside

Review Continued

• Kinematics Review worksheet• Relative Motion and Interval Questions

handout

Where Do I Find More Questions?• Derivations

– Go over derivations!• General Big 4 Questions

– Big 4 Examples Handout– Foldable

• Acceleration due to Gravity– Review Worksheet

• Interval questions– Relative Motion and Intervals Handout

• 2 Object Problems– Big 4 Examples Handout #7– Review worksheet

• Relative Motion– Relative Motion and Intervals Handout

The plan

• 1 – Derivation• 2 – Problem Solving & 2 Part Questions• 3 - Acceleration due to Gravity• 4 – Interval questions• 5 – 2 Object Problems• 6 – Relative Motion• 7 – Review• 8 - Test