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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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