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acceleration, velocity and position of an object

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An object moves along the x-axis with initial position x(0)=2. The velocity of the object at time t is greater than or equal to 0 is given by v(t)=sin((pi/3)t).
a.) What is the acceleration of the object at time t=4?
b.) Consider the following two statements.
Statement I: For 3<t<4.5, the velocity of the object is increasing.
Statement II: For 3<t<4.5, the speed of the object is decreasing.

Are either or both there statements correct? For each statement, provide
a reason why it is correct or not correct.
c.) What is the total distance traveled by the object over the time interval 0 is < or = to t which is < or = to 4?
d.) What is the position of the object at time t=4?

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Solution Summary

The solution is comprised of detailed explanations of an AP calculus practice problem dealing with the acceleration, velocity, and position of an object moving along x-axis. It is an application of derivative and integral.

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AP Calc Practice Problem
An object moves along the x-axis with initial position x(0)=2. The velocity of the object at time t is greater than or equal to 0 is given by v(t)=sin((pi/3)t).
a.) What is the acceleration of the object at time t=4?

Therefore, at t = 4,

b.) Consider the following two statements.
Statement I: For ...

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