# 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 objectβs velocity function given that the initial velocity is .

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**Q2: **

An objectβs acceleration is given by . Find the objectβs velocity function if its initial velocity is .

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**Q3: **

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

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**Q4: **

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

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**Q5: **

If the velocity of an object is given by , find the objectβs 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 objectβs 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 objectβs position given that .

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**Q8: **

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

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**Q9: **

An objectβs acceleration is given by . The objectβs initial velocity is . Find the objectβs velocity function.

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**Q10: **

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

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