Kinematics
AP Physics C
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Kinematics is a way of describing the motion of objects without describing the causes. You can describe an object's motion: In words. Mathematically.
Typology: Study notes
2021/2022
1 / 17
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Kinematics and more Study notes Kinematics in PDF only on Docsity!
Kinematics
AP Physics C
Defining the important variables Kinematics
is a way of describing the motion of objects
without describing the causes. You can describe anobject’s motion: In words^
Mathematically
Pictorially
Graphically
No matter HOW we describe the motion, there are several KEY VARIABLESthat we use.
m/s Final velocity v
m/s/s Acceleration due togravity g or ag
m/s Initial velocity vo
m Displacement x or y
m/s/s Acceleration a
s Time t
Units Variable Symbol
Kinematic
atv v
atv v vv t v t a^ o
o
o
+=
=− − → ∆ = ∆
Kinematic #1 Example:
A boat moves slowly out of a marina (so as to notleave a wake) with a speed of 1.50 m/s. As soon as itpasses the breakwater, leaving the marina, it throttles upand accelerates at 2.40 m/s/s
a = 2.40 m/s/s^ t = 5 s
v =? v= 1.50 m/so
What do Iwant? a) How fast is the boat moving after accelerating for 5 seconds? What do Iknow?
=
+= =v v atv v^ o
) (^5) )( (^40). (^2) () (^50). (^1) ( 13.5 m/s
Does all this make sense?
AbhA)^5.^1 )(^5 (^ =→= mA (^50). (^7) =
bhA^ mA 30
1 )^12 )(^5 (^2
13.5 m/s 1.5m/s
m
A
Abh
A^50.^7
Total displacement = 7.50 + 30 = 37.5 m = Total AREA under the line.
Interesting to Note
vt tv xx
att tv xx
at tv xxoxo oxo^ oxo
∆+ ++= ++= +=
(^21 )
A = HB
A=1/2HB
Most of the time, x
=0, but if it is noto don’t forget to ADD in the initialposition of the object.
Common Problems Students Have^ I don’t know which equation to choose!!!
x v^ t Missing Variable Equation
atv v^ o^
+=
(^21) at 2 tvx x^
++oxo
)( 22 2
o o^
xxa vv
− +=
Kinematics for the VERTICAL Direction All 3 kinematics can be used to analyze
one
dimensional motion
in either the X direction OR the
y direction.
) ( 2 ) ( 2
1 2
1 2
o oyy o ox
oyo
oxo
oyy o
yy g vv xx a vv
gt tv yy at tv xx
gtv vat vv
− += →− +=
++ =→ ++ =
+= →+ =
Examples A stone is dropped at rest from the top of a cliff. It isobserved to hit the ground 5.78 s later. How highis the cliff? g = -9.8 m/s^ y=0 mo t = 5.78 s
2
y =? v= 0 m/soy
What do Iwant? What do Iknow?
Which variable is NOT given andNOT asked for?^ Final Velocity!
21 gt 2
tvy
y^
++=oyo
=y y
)( 0 ( -163.7 mH =163.7m
Examples A pitcher throws a fastball with a velocity of 43.5 m/s. It isdetermined that during the windup and delivery the ball coversa displacement of 2.5 meters. This is from the point behind thebody when the ball is at rest to the point of release. Calculatethe acceleration during his throwing motion. x = 2.5 m^ v = 43.5 m/s
a =? v= 0 m/so
What do Iwant? What do Iknow?
Which variable is NOT given andNOT asked for?
TIME
) 2 (^2 2
o o^
xxa vv
− += =
− += a
a^
) (^05). (^2) ( 2 (^05). 43
(^22) 378.5 m/s/s
Examples A car accelerates from 12.5 m/s to 25 m/s in 6.0seconds. What was the acceleration? v = 25 m/s^ t = 6s
a =? v= 12.5 m/so
What do Iwant? What do Iknow?
Which variable is NOT given andNOT asked for?
DISPLACEMENT^ atvv +=o^ +=a^ = a
) (^6) ( 5
. 12 25^ 2.08 m/s/s
Kinematics and Calculus Let’s take the “derivative”of kinematic #2assuming the objectstarted at x = 0.
a atvd dt atvv dva dt
attvd dt dxv dt
att vx^ o
ox ox
+^ = += ==
+= ==
) ( 1 )^2 1 2 (^0
2 2