{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter_2

# Chapter_2 - Chapter 2 Motion Along a Straight Line In this...

This preview shows pages 1–6. Sign up to view the full content.

Chapter 2 Motion Along a Straight Line In this chapter we will study 1-dimensional kinematics i.e. how objects move along a straight line. The following parameters will be defined: Displacement Average velocity Average Speed Instantaneous velocity Average and instantaneous acceleration Special case: motion with constant acceleration --- we will develop the equations that give us the velocity and position at any time. Example: free fall motion Finally we will study a graphical integration method that can be used to analyze the motion when the acceleration is not constant (2-1)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Focus of this chapter: Motion will be along a straight line We will assume that the moving objects are “ particles ” i.e. all parts of an object move in the same way. The causes of the motion will not be investigated. Consider an object moving along a straight line taken to be the x-axis. The object’s position at time t is described by its coordinate x(t) defined with respect to the origin O (x=0). The coordinate x can be positive or negative (2-2) x 1 =-2m x 2 = 3m
Displacement. If an object moves from position x 1 to position x 2 , the change in position is described by the displacement For example if x 1 = 5 m and x 2 = 12 m then Δ x = 12 – 5 = 7 m. The positive sign of Δx indicates that the motion is along the positive x-direction If x 1 = 5 m and x 2 = 1 m then Δx = 1 – 5 = -4 m. The negative sign of Δx indicates that the motion is along the negative x-direction Displacement is a vector quantity that has both magnitude and direction. In this restricted one-dimensional motion the direction is described by the algebraic sign of Δx 2 1 x x x ∆ = - Note: The actual distance for a trip is irrelevant as far as the displacement is concerned For example an object moves from x 1 = 5 m to x 2 = 200 m and then back to x 2 = 5 m. The total distance covered is 2×195 = 390 m, the displacement Δ x = 0m (2-3) . . . O x 1 x 2 x -axis motion Δx

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Average Velocity We plot position x (t) as function of time t for a moving animal. We can get an idea of “ how fast ” the animal moves from one position x 1 at time t 1 to a new position x 2 at time t 2 by determining the average velocity between t 1 and t 2 . Here x 2 and x 1 are the positions x(t 2 ) and x(t 1 ), respectively. The time interval Δt is defined as : Δt = t 2 – t 1 The units of v avg are: m/s Example: x(0) = -5m, x(4)= 2m v avg = [2-(-5)]/(4-0) = 1.75 m/s 2 1 2 1 avg x x x v t t t - = = - (2-4)
Graphical determination of v avg On an x versus t plot we can determine v avg from the slope of the straight line that connects point ( t 1 , x 1 ) with point ( t 2 , x 2 ). In the plot below, t 1 =1 s, and t 2 = 4 s. The corresponding positions are : x 1 = - 4 m and x 2 = 2 m 2 1 2 1 2 ( 4) 6 m 2 m/s 4 1 3 s avg x x v t t - - - = = = = - - Average Speed s avg The average speed is defined in terms of the total distance traveled in a time

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 28

Chapter_2 - Chapter 2 Motion Along a Straight Line In this...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online