A particle at the origin has an initial velocity of . If its acceleration is given by , find the position of the particle after 1 second.

The function describing the acceleration of a spacecraft with respect to time is

Determine the function describing the position of a spacecraft given that the initial acceleration is 0, the initial velocity is 3, and the initial position is 9.

Determine the position function for a particle whose velocity is given by the equation

and whose initial position is 10.

A particle is moving in a straight path with a constant initial velocity. The particle is then subjected to a force causing a time-dependent acceleration given as a function of time:

After 10 seconds, the particle has a velocity equal to meters-per-second. Find the initial velocity in terms of the constants , and

Units are all in S.I. (meters, seconds, meters-per-second, etc.)

Given a particle with an acceleration at time to be . With initial conditions and where is the velocity at time , and is position of the particle at time .

Find the position at time .

Find the average value of the function on the interval

Find the velocity function given the following information:

The acceleration function is ;

What is the position function if the initial position is 0 and the velocity function is given by ?

Find the integral which satisfies the specific conditions of