# Worksheet: Linear Motion with Integration

In this worksheet, we will practice using integration to get the average and instantaneous velocities and displacement vectors of a particle in straight-line motion.

Q1:

If the acceleration of an object is given by , find the object’s velocity function given that the initial velocity is .

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Q2:

An object’s acceleration is given by . Find the object’s velocity function if its initial velocity is .

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Q3:

If the acceleration of an object is given by , find the object’s position function given that the initial velocity is .

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Q4:

If the acceleration of an object is given by , find the object’s velocity function, given that the initial velocity is .

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Q5:

If the velocity of an object is given by , find the object’s position function given that the initial position is .

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Q6:

If the acceleration of an object is given by , find the function describing the object’s position given that its initial position and velocity are both zero.

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Q7:

The velocity of an object is given by . Find the function describing the object’s position given that .

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Q8:

If the acceleration of an object is given by , find the function describing the object’s position given that its initial position is and initial velocity .

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Q9:

An object’s acceleration is given by . The object’s initial velocity is . Find the object’s velocity function.

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Q10:

If the acceleration of an object is given by , find the function describing the object’s velocity function given that its initial velocity is zero.

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