Ch1: 1D Kinematics 1.Recall main points: position, displacement, velocity and acceleration (geometrically and algebraically) 2.Discuss Pre-lecture and.

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