Calculus

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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