Calculus

Displacement, Velocity, Acceleration

Finding Acceleration Given Velocity

         

The velocity of a particle at time t t is given by f(t)=sin5(2t). f(t) = \sin ^{5} \left(2t \right). What is the acceleration of the particle at time t=1?t=1?

At time t t, the velocity of a motorcyclist is v(t)=5436et v(t) = 54 - 36e^{-t} mph. What is his acceleration when his velocity is 11?

The position of a particle at time t t is given by f(t)=t6+3t3 f(t) = t^{6} + 3 t^{3} . What is the acceleration of the particle at time t=2?t=2?

The velocity of a particle at time t t is given by a function f(t) f(t) which satisfies (2+f(t))e(t2)f(t)=9. \left( 2 + f(t) \right) e^{ (t-2) f(t)} = 9 . If f(t) f(t) is differentiable at time 2,2, what is the particle's acceleration at time 2?2?

The velocity of a particle at time t t is given by f(t)=t3t3+1. \displaystyle{ f(t) = \frac{t^{3}}{ t^{3} + 1} }. If the acceleration of the particle at time t=2 t=2 is A,A, what is 81A? 81 A ?

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