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Kinematics: Acceleration, Speed & Velocity Mr. Holmes

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Kinematics Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Kinematics is a branch of mechanics, the study of the motion of objects. The goal of any study of kinematics is to develop sophisticated mental models that serve to describe (and ultimately, explain) the motion of real-world objects.

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Speed is related to a distance traveled and the amount of time it takes to travel that distance Speed is calculated by the equation s=d/t.

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S= speed D= distance T= time

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The velocity of an object is similar to the speed, however it includes the direction in which the object is moving. The equation for velocity is the same as that of speed, v=d/t

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To begin, let's look at constant velocity. In the first graph below you can see the result of an object moving at a constant velocity of 6 m/s for a time interval of 8 seconds.

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In order to find the displacement after 8 seconds, we will find the area between the graph and the horizontal axis, as shaded in the diagram at the right, above. Displacement = area of rectangle = 6 m/s x 8 s = 48 m Since there is no acceleration, this is equivalent to using the formula d = v · t

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Consider a car moving with a constant, rightward (+) velocity - say of +10 m/s. A car moving with a constant velocity is a car with zero acceleration.

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If the velocity-time data for such a car were graphed, then the resulting graph would look like the graph below. Note that a motion described as a constant, positive velocity results in a line of zero slope (a horizontal line has zero slope) when plotted as a velocity-time graph. Furthermore, only positive velocity values are plotted, corresponding to a motion with positive velocity.

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When you think of acceleration, you probably think of something speeding up. Acceleration could also be an object slowing down. Acceleration is a change in velocity including how fast something is moving or a change in moving direction

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To calculate acceleration, you need to take the change in velocity or speed and divide it by the amount of time over which the change occurred. »acceleration = (change in velocity) / time

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Now let's look at an example where there is acceleration. We'll begin with the case where an object starts from rest.

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In order to find the displacement after 8 seconds, we will find the area between the graph and the horizontal axis, as shaded in the diagram at the right, above. Displacement = area of triangle = (8 s x 10 m/s)/2 = 40 m Since there is acceleration, and v i = 0, this is equivalent to using the formula d = 1/2 · t · (v f - v i )

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How is the change in velocity calculated? I’m glad you asked!!!!! Change in velocity = final velocity – initial velocity = v f – v i

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Now you can calculate accelerationNow you can calculate acceleration A= (v f – v i )A= (v f – v i ) t

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An object starting from a nonmoving position will have an initial velocity of “0” zero.An object starting from a nonmoving position will have an initial velocity of “0” zero. The unit of acceleration is m/s 2. How do you come up with that?The unit of acceleration is m/s 2. How do you come up with that? Glad you asked.Glad you asked.

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Calculating Negative Acceleration This is used for objects that are slowing down. Imagine that a skateboarder is traveling at a speed of 6 m/s and comes to a complete stop in 2 seconds. What is his acceleration?

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Let’s Practice

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Calculating Positive Acceleration Positive Acceleration can found in objects that are speeding up. An objects starts from rest and speeds up to 80 m/s in 20 s. What is the acceleration?

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Find the acceleration of a long distance runner starting out at a velocity of 500 meters per second/west. In the next 2 minutes, he increases his velocity to 700 meters per second/west. What is his rate of acceleration?

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A swimmer speeds up from 1.1 m/s to 1.3 m/s during the last 20 seconds of a workout. What is the swimmer’s acceleration?

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While walking to school, you approach an intersection and slow down from 2 m/s to a stop in 3 seconds. What was your acceleration during this time interval?

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