# Worksheet: Planar Motion Using Parametric Equations

In this worksheet, we will practice describing motion of a particle along a curve defined by parametric functions.

Q1:

A particle has a position defined by the equations and . Find the speed of the particle at .

• A27
• B
• C
• D585
• E567

Q2:

A particle has a position defined by the equations and . Find the velocity vector of the particle at .

• A
• B
• C
• D
• E

Q3:

A moving particle along a curve is defined by the two equations and . Find the acceleration vector of the particle at .

• A
• B
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• E

Q4:

A moving particle is defined by the two equations and . Find the magnitude of the acceleration of the particle at .

• A
• B232
• C
• D
• E200

Q5:

A moving particle is defined by the two equations and . Find the magnitude of the acceleration of the particle at .

• A
• B193
• C
• D
• E13

Q6:

Given that the position of a moving particle is defined by the parametric equations and , find the speed of the particle at to the nearest tenth.

• A
• B
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• D
• E

Q7:

If a particle is moving on a curve defined by the parametric equations and , find the time, to the nearest tenth, at which .

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• E

Q8:

If a particle is moving on a curve defined by the parametric equations and , find the time, to the nearest tenth, at which .

• A
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• E

Q9:

Suppose that a particle is moving on a curve defined by the parametric equations and . If the particle is initially at horizontal displacement , find the minimum horizontal displacement from .

• A
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• E

Q10:

Suppose that a particle is moving on a curve defined by the parametric equations and . If the particle is initially at vertical displacement , find the maximum positive vertical displacement from .

• A
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• E

Q11:

A particle starts its motion at the point . The particle’s velocity is given by the parametric equations and , where is the time after the particle started its motion. Find the position vector of the particle at time .

• A
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• E

Q12:

The position of a particle is defined by and . Find the speed of the particle when , giving your answer to two decimal places.

Q13:

A particle moves along a curve defined by the parametric equations and . What is the shape of the trajectory of the particle?

• AA parabola
• BA cubic curve
• CAn exponential curve
• DA hyperbola
• EA logarithmic curve

Q14:

The acceleration of a particle in a coordinate grid is given by the parametric equations and . At the time , the position of the particle is given by and and the velocity of the particle is given by and . Find the parametric equations which represent the position of the particle at time .

• A
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• E

Q15:

A particle’s velocity is given by the parametric equations and . Find the acceleration vector of the particle at .

• A
• B
• C
• D
• E