Jan. 28-Feb. 1, 2013
MotionqEverything moves!
Motion is one of the main topics in Physics I
qSimplification: Consider a moving object as a particle, i.e. it moves like a particle—a “point object”
LAX
Newark
Jan. 28-Feb. 1, 2013
One Dimensional Position rq Motion can be defined as the change of position over
time.q How can we represent position along a straight line?q Position definition:
n Defines a starting point: origin (r = 0), r relative to originn Direction: positive (right or up), negative (left or down)n It depends on time: t = 0 (start clock), r(t=0) does not have to
be zero.q Position has units of [Length]: meters.
r = + 2.5 m i r = - 3 m i
For motion along a straight line, the direction is represented simply by + and – signs.
+ sign: Right or Up.- sign: Left or Down.
Jan. 28-Feb. 1, 2013
Displacementq Displacement is a change of position in time.q Displacement:
n f stands for final and i stands for initial.q It is a vector quantity.q It has both magnitude and direction: + or - signq It has units of [length]: meters.
)()( iiff trtrr !!! −=Δ
r1 (t1) = + 2.5 m ir2 (t2) = - 2.0 m iΔr = -2.0 m - 2.5 m = -4.5 m ir1 (t1) = - 3.0 m ir2 (t2) = + 1.0 m iΔr = +1.0 m + 3.0 m = +4.0 m i
Jan. 28-Feb. 1, 2013
Distance and Position-time graph
q Displacement in spacen From A to B: Δr = rB – rA = 52 m – 30 m i = 22 m in From A to C: Δr = rc – rA = 38 m – 30 m = 8 m i
q Distance is the length of a path followed by a particlen from A to B: d = |rB – rA| = |52 m – 30 m| = 22 mn from A to C: d = |rB – rA|+ |rC – rB| = 22 m + |38 m – 52 m| = 36 m
q Displacement is not Distance.
Jan. 28-Feb. 1, 2013
Velocityq Velocity is the rate of change of position.q Velocity is a vector quantity.q Velocity has both magnitude and direction.q Velocity has a unit of [length/time]: meter/second.q We will be concerned with three quantities, defined as:
n Average velocity
n Average speed avgtotal distances
t=
Δ
txx
txv if
avg Δ−
=ΔΔ=
displacement
distance
Jan. 28-Feb. 1, 2013
Average Accelerationq Changing velocity (non-uniform) means an
acceleration is present.q Acceleration is the rate of change of velocity.q Acceleration is a vector quantity.q Acceleration has both magnitude and direction.q Acceleration has a dimensions of length/time2: [m/s2].q Definition:
n Average acceleration
n Instantaneous acceleration if
ifavg tt
vvtva
−−
=ΔΔ=
Jan. 28-Feb. 1, 2013
Special Case: Motion with Uniform Acceleration (our typical case)
q Acceleration is a constantq Kinematic Equations (which
we will derive in a moment)
tavv !!! += 0
221
00 tatvrr !!!! ++=
xavv !!!! Δ+= 220
2
Jan. 28-Feb. 1, 2013
Problem-Solving Hintsq Read the problemq Draw a diagram
n Choose a coordinate system, label initial and final points, indicate a positive direction for velocities and accelerations
q Label all quantities, be sure all the units are consistentn Convert if necessary
q Choose the appropriate kinematic equationq Solve for the unknowns
n You may have to solve two equations for two unknownsq Check your results
xavv Δ+= 220
2
atvv += 0
221
0 attvx +=Δ
Jan. 28-Feb. 1, 2013
Exampleq An airplane has a lift-off speed of 30 m/s
after a take-off run of 300 m, what minimum constant acceleration?
q What is the corresponding take-off time?
xavv Δ+= 220
2
atvv += 02
21
0 attvx +=Δ xavv Δ+= 220
2
atvv += 02
21
0 attvx +=Δ
September 8, 2008
Free Fall Accelerationq Earth gravity provides a constant
acceleration. Most important case of constant acceleration.
q Free-fall acceleration is independent of mass.
q Magnitude: |a| = g = 9.8 m/s2
q Direction: always downward, so ag is negative if define “up” as positive,a = -g = -9.8 m/s2
q Try to pick origin so that yi = 0
y
September 8, 2008
Free Fall Accelerationq Two important equation:
q Begin with t0 = 0, v0 = 0, y0 = 0q So, t2 = 2|y|/g same for two balls!q Assuming the leaning tower of Pisa is
150 ft high, neglecting air resistance,t = (2´150´0.305/9.8)1/2 = 3.05 s
y
gtvv −= 0
20 0
12
y y v t gt= + −0
Jan. 28-Feb. 1, 2013
Summaryq This is the simplest type of motionq It lays the groundwork for more complex motionq Kinematic variables in one dimension
n Position r(t) m Ln Velocity v(t) m/s L/Tn Acceleration a(t) m/s2 L/T2
n All depend on timen All are vectors: magnitude and direction vector:
q Equations for motion with constant acceleration: missing quantitiesn r
n v
n t
tavv !!! += 0
221
00 tatvrr !!!! ++=
)(2 020
2 xxavv !!!!" −+=