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Classical Mechanics

1D Kinematics

Position, Velocity, and Acceleration


Suppose that the displacement \(s\) of an aeroplane can be expressed as a function of time \(t\) in the following way: \[ s(t) = 8 t^2 + 10 t .\] What is the magnitude of the acceleration of the object?

Point \(P\) moves along the \(x\)-axis in such a way that its position is \(x(t)=6-2t,\) where \(t\) denotes elapsed time. If \(t\) has changed from \(0\) to \(12,\) what is the average velocity of point \(P?\)

Stacey was driving her car at a speed of \(30\text{ mph}\) on a straight avenue, when suddenly she noticed that she had forgotten to bring her purse. So she immediately made a U-turn and headed back to her house. Now she is almost home, and she looks at her watch, recognizing that \(30\) minutes has passed from the moment of the U-turn. If her current speed is \(40\text{ mph},\) what is her average acceleration for the \(30\) minutes on her way back home?

John is jogging from his home to the park, and back. If the distance between his home and the park is \(700\) yards and John has jogged for a total of \(14\) minutes, what is his average velocity, \(\vec{v}\)?

I'm driving along at a constant speed in my 3-meter-long car when I notice that I am accidentally driving through a red light. If the rear end of my car passes under the light 0.3 seconds after the front end of my car, how fast am I driving in m/s?


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