Kinematics

MYP/Honors Physics

Defining the important variablesKinematics is a way of describing the motion of objects

without describing the causes. You can describe an object’s motion:

In wordsMathematically Pictorially GraphicallyNo matter HOW we describe the motion, there are several KEY VARIABLES that we use.

Symbol Variable Units

t Time s

a Acceleration m/s2

s, x, or y Displacement m

vi, vo, or v1 Initial velocity m/s

vf, v, or v2 Final velocity m/s

ag or g Acceleration due to gravity

m/s2

The 3 Kinematic equations

There are 3 major kinematic equations that can be used to describe the motion in DETAIL. All are used when the acceleration is CONSTANT.

Kinematic #1

atvv

atvvt

vv

t

va

i

i

f

f

if

This equation is the result of the definition of acceleration, a change in velocity over time.

Kinematic #1Example: A boat moves slowly out of a marina (so as to not

leave a wake) with a speed of 1.50 m/s. As soon as it passes the breakwater, leaving the marina, it throttles up and accelerates at 2.40 m/s2.

What do I know?

What do I want?

vi= 1.50 m/s vf = ?

a = 2.40 m/s2

t = 5 s

a) How fast is the boat moving after accelerating for 5 seconds?

13.5 m/s

Kinematic #22

21 attvs i

b) How far did the boat travel during that time?

37.5 m

Kinematic #3)(222 savv

if

What do I know?

What do I want?

vi= 12 m/s Δs = ?

a = -3.5 m/s2

Vf = 0 m/s

Example: You are driving through town at 12 m/s when suddenly a ball rollsout in front of your car. You apply the brakes and begin decelerating at 3.5 m/s2.

How far do you travel before coming to a complete stop?

20.6 m

Common Problems Students HaveI don’t know which equation to choose!!!

Equation Missing Variable

Δs or Δx

vf

t

2

21 attvs i

savv if 222

ExamplesA stone is dropped at rest from the top of a cliff. It is

observed to hit the ground 5.78 s later. How high is the cliff?

What do I know?

What do I want?

vi= 0 m/s ∆s = ?

a = -9.8 m/s2

t = 5.78 s

Which equation relates what is given and what is needed?

2

21 attvs i

s

s 2)78.5(9.4)78.5)(0(

-164 m

H =164 m

A) -164 mB) 327 mC) 164 mD) -327 mE) None of the above

ExamplesA pitcher throws a fastball with a velocity of 23.5 m/s. It is

determined that during the windup and delivery the ball covers a displacement of 0.95 meters. This is from the point behind the body when the ball is at rest to the point of release. Calculate the acceleration during his throwing motion.

What do I know?

What do I want?

vi= 0 m/s a = ?

∆s = 0.95 m

vf = 23.5 m/s

Which equation relates what is given and what is needed?

savv if 222

a

a )95(.205.23 22

291 m/s2

A) 291 m/s2 B) 24.7 m/s2

C) 22.3 m/s2

D) 44.7 m/s2

E) None of the Above

ExamplesHow long does it take a car at rest to cross a 35.0 m

intersection after the light turns green, if the acceleration of the car is a constant 2.00 m/s2?

What do I know?

What do I want?

vi= 0 m/s t = ?

∆s = 35 m

a = 2.00 m/s2

t

t 2)2(21)0(35

2

21 attvs i

5.92 s

Which equation relates what is given and what is needed?

A) 35.0 sB) 17.5 sC) 8.75 sD) 2.95 sE) None of the above

ExamplesA car accelerates from 12.5 m/s to 25 m/s in 6.0

seconds. What was the acceleration?

What do I know?

What do I want?

vi= 12.5 m/s a = ?

vf = 25 m/s

t = 6s

Which equation relates what is given and what is needed?

2.08 m/s2

A) 1.35 m/s2

B) 6.25 m/s2

C) 6.50 m/s2

D) 2.08 m/s2

E) None of the above