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Calculus

Displacement, Velocity, Acceleration

Concept Quizzes

Average Velocity
Instantaneous Velocity
Finding Acceleration Given Velocity
Displacement, Velocity, Acceleration Word Problems

Challenge Quizzes

Displacement, Velocity, Acceleration (Derivatives): Level 2 Challenges
Displacement, Velocity, Acceleration (Derivatives): Level 3 Challenges

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 $t?$

v(t) = (8 t + 3) \text{ m/s}

v(t) = (8 t + 4) \text{ m/s}

v(t) = (8 t + 14) \text{ m/s}

v(t) = (3 t + 14) \text{ m/s}

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by Brilliant Staff

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?

44 \text{ m/s}

41 \text{ m/s}

43 \text{ m/s}

42 \text{ m/s}

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by Brilliant Staff

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 $t?$

v(t) = (15 t^2 + 12 t + 5) \text{ m/s}

v(t) = (10 t^2 + 24 t + 5) \text{ m/s}

v(t) = (15 t^2 + 24 t + 5) \text{ m/s}

v(t) = (15 t^2 + 12 t + 17) \text{ m/s}

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by Brilliant Staff

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?

34 \text{ m/s}

32 \text{ m/s}

33 \text{ m/s}

35 \text{ m/s}

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by Brilliant Staff

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?

777 \text{ m/s}

775 \text{ m/s}

776 \text{ m/s}

774 \text{ m/s}

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by Brilliant Staff