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Displacement, Velocity, Acceleration

How fast are you moving? How fast is how fast you are moving changing? Displacement, velocity, and acceleration form the art of understanding movement, Calculus-style.

Instantaneous Velocity

         

The position (in meters) of an object moving in a straight line is given by \(s(t)=4t^2 + 3t + 14,\) where \(t\) is measured in seconds. What is the equation of the instantaneous velocity \(v(t)\) of the particle at time \(t?\)

The position in meters of a particle at time \(t\) is given by \(s(t)=t^2 + 3t\), where \(t\) is measured in seconds. What is the instantaneous velocity of the particle (in m/s) at time \(t=19\) seconds?

The position (in meters) of an object moving in a straight line is given by \(s(t)=5t^3 + 12t^2 + 5t + 17,\) where time \(t\) is measured in seconds. What is the equation of the instantaneous velocity \(v(t)\) of the particle at time \(t?\)

The position (in meters) of a particle moving in a straight line is given by \(s(t)=t^2 + 8t + 18,\) where \(t\) is measured in seconds. What is the instantaneous velocity of the particle at \(t=12\) seconds?

The position (in meters) of a particle moving in a straight line is given by \(s(t)=4t^3+6t+2,\) where \(t\) is measured in seconds. What is the instantaneous velocity of the particle at \(t=8\) seconds?

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