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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

Finding Acceleration Given Velocity

The velocity of a particle at time $t$ is given by $f(t) = \sin ^{5} \left(2t \right).$ What is the acceleration of the particle at time $t=1?$

10 \sin^{5}2 \cos2

10 \cos^{5}2

10 \sin^{4}2 \cos2

10 \sin^{4}2

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At time $t$ , the velocity of a motorcyclist is $v(t) = 54 - 36e^{-t}$ mph. What is his acceleration when his velocity is 11?

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The position of a particle at time $t$ is given by $f(t) = t^{6} + 3 t^{3}$ . What is the acceleration of the particle at time $t=2?$

2064 1032 516 210

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The velocity of a particle at time $t$ is given by a function $f(t)$ which satisfies $\left( 2 + f(t) \right) e^{ (t-2) f(t)} = 9 .$ If $f(t)$ is differentiable at time $2,$ what is the particle's acceleration at time $2?$

-63 99 11 63

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The velocity of a particle at time $t$ is given by $\displaystyle{ f(t) = \frac{t^{3}}{ t^{3} + 1} }.$ If the acceleration of the particle at time $t=2$ is $A,$ what is $81 A ?$

12 408 792 204

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