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Ch1
: 1D
Kin
emati
cs1. Recall main points: position, displacement, velocity
and acceleration (geometrically and algebraically)2. Discuss Pre-lecture and Check Points3. Examples of problems
1.1
Mai
n Po
ints
Position x of point P in 1D: Axis, Origin, Direction
Average velocity of P between times t1 and t2:
Instantaneous Velocity of P at time t:
Instantaneous acceleration of P at t:
1.1
Mai
n Po
ints
Graphical relationship from x to v to a. Example start with a=cst
a v
x
t t
t
-2m/s2
Slope= 2 m/s
Slope= -2 m/s
t=5s
t=5s
1 2 3
4 5
A
B
C
D
2
4
3
1
5 2, 3 and 4
6 2 and 3
Given a find v then x:
1.1
Mai
n Po
ints
Algebraic relationship from x to v=velocity to a=acceleration. Start with x(t)=2t-1
Meaning of the coef. 2 and -1. They depend on t=0 and origin of axis
Algebraic relationship from x to v to a. General case: for 1 D motion with no acceleration (cst velocity)
( )( ) 2
dx tv t
dt
( )( ) 0
dx ta t
dt
In general for x=At+B:
Second derivative /t:First derivative /time:
( )( )
dx tv t A
dt
( )( ) 0
dx ta t
dt
At t=0: (0)v A(0)x B
So that we define: 0 (0)x x B 0 (0)v v A
1.1
Mai
n Po
ints
Motion with constant a: from a to xGraphical x, v, a
Algebraic x, v, a
1.2
Dis
cuss
For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time?
1.2
Dis
cuss
Set up problem (always same way ): 1. Picture: Axes with origin and direction2. Equations relevant to problem and specified for axis choice3. Constraint Equations4. Solution
At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 m between t = 0 sec and t = 1 sec. How far does it move between t = 1 sec and t = 2 sec?
CheckPoint 2:
1.3
prob
lem
sRelative signs of v, a and relation to speed and slowing down or speeding up. Difference between the quantity and its magnitude.
Example. Throw an object up in the air.
A. How high does it go above release point, given vo?
1.3
prob
lem
s
1.3
prob
lem
sB. How long does it stay in the air, given vo?
Example. Throw an object up in the air, cont’d
Example. Two objects up in the air. Released same time, one from h at vo=0, the other from y=0 at vo After how long do they meet?
1.3
prob
lem
s
Example.1.
3 pr
oble
ms
Ch 1: Assignments
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