In part (b), acceleration is not constant. During the 1-h interval, velocity is closer to 80 km/h than 40 km/h. Thus, the average velocity is greater than in part (a).
Solving for final velocity from acceleration and time
We can derive another useful equation by manipulating the definition of acceleration:
Substituting the simplified notation for
and
gives us
Solving for
v yields
Calculating final velocity
An airplane lands with an initial velocity of 70.0 m/s and then decelerates at 1.50 m/s
2 for 40.0 s. What is its final velocity?
Strategy
First, we identify the knowns:
.
Second, we identify the unknown; in this case, it is final velocity
.
Last, we determine which equation to use. To do this we figure out which kinematic equation gives the unknown in terms of the knowns. We calculate the final velocity using
[link] ,
.
Solution
Substitute the known values and solve:
[link] is a sketch that shows the acceleration and velocity vectors.
Significance
The final velocity is much less than the initial velocity, as desired when slowing down, but is still positive (see figure). With jet engines, reverse thrust can be maintained long enough to stop the plane and start moving it backward, which is indicated by a negative final velocity, but is not the case here.
In addition to being useful in problem solving, the equation
gives us insight into the relationships among velocity, acceleration, and time. We can see, for example, that
Final velocity depends on how large the acceleration is and how long it lasts
If the acceleration is zero, then the final velocity equals the initial velocity (
v =
v0 ), as expected (in other words, velocity is constant)
If
a is negative, then the final velocity is less than the initial velocity
All these observations fit our intuition. Note that it is always useful to examine basic equations in light of our intuition and experience to check that they do indeed describe nature accurately.
Solving for final position with constant acceleration
We can combine the previous equations to find a third equation that allows us to calculate the final position of an object experiencing constant acceleration. We start with
Adding
to each side of this equation and dividing by 2 gives
Since
for constant acceleration, we have
Now we substitute this expression for
into the equation for displacement,
, yielding
Questions & Answers
I'm interested in biological psychology and cognitive psychology
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills