ObjectivesDefine velocity.Differentiate between speed and velocity.Create pictorial, physical, and mathematical models of motion problems.

VELOCITY In Figure 2-20a you can see the position of the jogger in red

shorts changes more than the jogger in blue shorts. In other words, for a fixed time interval, the displacement, ∆d, is greater for the jogger in red because she is moving faster.

  She covers a larger distance than the jogger in blue does in

the same amount of time.   Now, suppose that each jogger travels 100 m. The time

interval, ∆t, would be smaller for the jogger in red than for the one in blue.

  In Figure 2-20b the slope of the red jogger’s line is steeper

than the slope of the blue jogger’s line.

A steeper slope indicates a greater change in displacement during each time interval.

VELOCITY In a Position Time Graph, the unit of the slope is meter per second. In

other words, the slope tells how many meters the runner moved in 1 s.

  The slope is the change in position, divided by the time interval

during which that change took place, or (df – di) / (tf - ti), or Δd/Δt.

  When Δd gets larger, the slope gets larger; when Δt gets larger, the

slope gets smaller.  Average Velocity – is the ratio of the change of position to the time

interval during which it occurred. It is the slope of a Position Time Graph. It is a vector quantity.

v = d = df – di

t tf – ti

VELOCITY The symbol ≡ means that the left-hand side of the equation is defined by the right-

hand side.  It is a common misconception to say that the slope of a position-time graph gives

the speed of the object.   The slope of the position-time graph indicates the average velocity of the object and

not its speed.   Average Speed – is the absolute value of the slope of a position time graph. It is

how fast an object is moving without regard to its direction. It is a scalar quantity.  If an object moves in the negative direction, then its displacement is negative. The

object’s velocity will always have the same sign as the object’s displacement.

 Example 3 v = d = df – di = 12 – 0_ = 12_ = 1.714 m/s

t tf – ti 7 – 3.5 3.5

Do Practice Problems p. 45 # 25-28

INSTANTANEOUS VELOCITYInstantaneous Velocity – is a measure of

motion that tells the speed and direction of an object at a specific instant in time.

AVERAGE VELOCITY ON MOTION DIAGRAMS We will take our Slope Intercept form of a line (y = mx + b) and

convert it to an equation that fits with our displacement, time and velocity. The equation will be d = vt + di

  Equation of Motion for Average Velocity – states an object’s

position is equal to the average velocity multiplied by time plus the initial position. So d = vt + di

  Do 2.4 Section Review p. 47 # 29-33  Also from Chapter 3 of old book also in chapter 3 of new book Velocity Time Graph – a graph that can be used to plot the

velocity of an object versus the time and it determines the sign of the object’s acceleration. The area under the curve of a Velocity Time graph is the DISPLACEMENT. (p. 58-59 of new book)