Constant Velocity
Problem:
An object initially at rest experiences an acceleration of 1.5 m/(s^2) for six seconds, and then travels at that constant velocity for another eight seconds.
What is the object's average velocity over the fourteen second interval?
What is the object's average velocity over the fourteen second interval?
Graphs* and explanations:
*click on graph to enlarge it
XT Graph:
![Picture](/uploads/1/8/5/6/18566514/793543086.png?283)
This graph shoes the initial movement of the object and the constant velocity. The initial acceleration is during the first six seconds, during which the object travels 1.5 m/s^2 faster each second. The constant velocity is from eight seconds onward, at which point the object travels consistently.
Vt graph:
![Picture](/uploads/1/8/5/6/18566514/580359109.png?288)
The velocity graph shows hoe the the velocity changes according to the length of time that it has taken for the object to travel. The initial velocity is constantly increasing for the first six seconds. The constant velocity is for the next eight seconds, during which the object travels the same distance each second.
At Graph:
![Picture](/uploads/1/8/5/6/18566514/247202788.png)
This graph shoes the initial acceleration, and then once the object travels at constant velocity, the acceleration changes to zero.
Motion Map:
![Picture](/uploads/1/8/5/6/18566514/805824014.png)
This shows the increasing velocity of the object (where the points are farther apart), to the constant velocity (the consistent space between the points).
Equations:
V= ( Δx)/t = [(1/2∗b∗h)+(l∗w)]/14
V = [(3∗9)+(8∗9)]/14
V = (27+72)/14
V = 99/14
V = 7.1 m/s is the average velocity of the object.
V = [(3∗9)+(8∗9)]/14
V = (27+72)/14
V = 99/14
V = 7.1 m/s is the average velocity of the object.
Equation Explanations:
Δx: stands for the displacement; represents the area created in the velocity graph; represents the horizontal displacement of the object.
V: velocity
t: time
Brackets: The first set of numbers in parenthesis is the triangular area, while the second set of numbers indicates the area of the rectangle.
V: velocity
t: time
Brackets: The first set of numbers in parenthesis is the triangular area, while the second set of numbers indicates the area of the rectangle.