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 \(P?\)

At 5:30 pm, Stacey was driving her car at a speed of \(30\text{ mph}\) on a straight avenue. Suddenly she notices that she had forgotten to bring her purse, so she immediately makes a U-turn and heads back to her house. Now she looks at her watch, which says 6:00 pm. If her current speed is \(40\text{ mph},\) what is the magnitude of her average acceleration from 5:30 to 6:00 pm?

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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