Initial-value problems arise in many applications. Next we consider a problem in which a driver applies the brakes in a car. We are interested in how long it takes for the car to stop. Recall that the velocity function
is the derivative of a position function
and the acceleration
is the derivative of the velocity function. In earlier examples in the text, we could calculate the velocity from the position and then compute the acceleration from the velocity. In the next example we work the other way around. Given an acceleration function, we calculate the velocity function. We then use the velocity function to determine the position function.
Decelerating car
A car is traveling at the rate of
ft/sec
mph) when the brakes are applied. The car begins decelerating at a constant rate of
ft/sec
2 .
How many seconds elapse before the car stops?
How far does the car travel during that time?
First we introduce variables for this problem. Let
be the time (in seconds) after the brakes are first applied. Let
be the acceleration of the car (in feet per seconds squared) at time
Let
be the velocity of the car (in feet per second) at time
Let
be the car’s position (in feet) beyond the point where the brakes are applied at time
The car is traveling at a rate of
Therefore, the initial velocity is
ft/sec. Since the car is decelerating, the acceleration is
The acceleration is the derivative of the velocity,
Therefore, we have an initial-value problem to solve:
Integrating, we find that
Since
Thus, the velocity function is
To find how long it takes for the car to stop, we need to find the time
such that the velocity is zero. Solving
we obtain
sec.
To find how far the car travels during this time, we need to find the position of the car after
sec. We know the velocity
is the derivative of the position
Consider the initial position to be
Therefore, we need to solve the initial-value problem
Integrating, we have
Since
the constant is
Therefore, the position function is
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.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
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
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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