Uniformly Accelerated Motion

​How is velocity obtained using the displacement versus time graph?

UNIFORMLY ACCELERATED MOTION

MELC'S:

1. Compare and contrast the Aristotelian and Galilean conceptions of vertical motion, horizontal motion, and projectile motion.

2. Explain how Galileo inferred that objects in a vacuum fall with uniform acceleration, and that force is not necessary to sustain horizontal motion.

​The graph of velocity versus time must be a horizontal line. The displacement may be obtained by computing the area bounded by the horizontal line and the time axis.

Displacement versus time

​How is velocity obtained using the displacement-versus-time graph?

VELOCITY-VERSUS-TIME GRAPH FOR UNIFORMLY ACCELERATED MOTION WITH AN INITIAL VELOCITY V₀

​There are times that the slope (and therefore acceleration), is negative. What does a negative slope mean?

Negative Slope

​Suppose a male student plans to stroll along a straight road. He has two choices of direction to move. Considering his starting position as the origin, he can move either to the left or to the right, His movement to the left of the origin is designated as the negative direction, and his movement to the right as the positive direction.

​A positive slope representing either a velocity or acceleration means that the velocity or acceleration is directed to the right of the origin. a negative slope means that the velocity or acceleration is directed to the left of the origin. Note that negative acceleration does not necessarily mean deceleration.

​Whenever the velocity and acceleration of a body are in the same direction (and hence the same sign, whether negative or positive), the body is speeding up. Thus negative acceleration is directed (and therefore means acceleration in a negative direction. Whenever velocity and acceleration are oppositely directed(and therefore have signed), the body is slowing down and is said to be decelerating.

The graph below is a velocity-time graph of a student as he walks from his dormitory to his school. Describe the type of motion for intervals A-B,

B-C, and C-D. How far is the school from the dormitory?

Solution:

A-B is uniformly accelerated motion

​B-C is uniform motion, and C-D is uniformly decelerated motion.

​Let d_T be the distance from the school to the student's dormitory. To get these distances, compute the total area bounded by the graph. Recall the following formulas for finding the Area (A).

Α_triangle=1/2(base)(height) Α_rectangle=(length)(width)

Therefore,

d_T=d_a-b+d_c-d

_dA-B=1/2(4.0m/s)(20.0s)=40.0m

​d_B-C =(4.0m/s)(80.0s)=320.0 m

d_C-D=1/2(4.0m/s)(60.0s)=120.0 m

dT=40.0m+320.0m+120.0m=480.0m

​Practice Exercise: Using the velocity-time graph in the sample problem, construct the corresponding displacement-time graph Also, determine the acceleration for each time interval.

​Performance Task's:

1. How can the motion of an object be observed, described, and measured?

2. How do you describe your day to day motion?

3. How can I make sure of Newton's Law of motion to my advantage?

4. Why are the conservation laws in physic's important?