Exercises for Question Type 1: Determining speed of an object for a given trajectory - IB

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Exercises for Question Type 1: Determining speed of an object for a given trajectory - IB

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Question 1

Kinematics with vectors

An object moves with position vector r (t) = 4 - 2 1 + t - 3 62 . Calculate its speed.

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Question 2

An object follows the path r (t) = (2, 1, - 1) + t (3, 4, 5) . Determine whether it passes through the point (11, 13, 19), and find t if it does.

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Question 3

Determine whether the line r (t) = (5, 5, 5) + t (2, - 3, 4) passes through the point (17, - 1, 21) and find the corresponding value of t if it does.

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Question 4

An object moves with a position vector given by r (t) = 3 - 2 5 + t - 2 31 . Determine whether the object reaches the point (- 1, 7, 8), and find the value of t if it does.

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Question 5

An object travels on the path r (t) = (0, 0, 0) + t (2, 2, 1), where t is time. Find the speed of the object.

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Question 6

Find the speed of an object moving along r (t) = 123 + t 05 - 12 .

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Question 7

Does the line r (t) = (0, 0, 0) + t (1, 2, 4) pass through the point (7, 14, 28) ? If so, find the value of t .

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Question 8

An object moves with constant velocity such that its position vector at time t is given by r (t) = 101 + t 872 . Find the speed of the object.

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Question 9

Does the path r (t) = (1, 0, 1) + t (8, 7, 2) pass through the point (17, 14, 5) ? If so, find the time t .

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Question 10

Given r (t) = - 3 50 + t 6 - 2 1, determine the speed of the object.

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Question 11

An object moves along the path r (t) = (2, - 1, 3) + t (4, 0, - 3) . Calculate its constant speed.

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Question 12

For an object with position vector r (t) = - 1 24 + t 5 - 1 3, determine if the object ever reaches the point (9, - 3, 13) . Find the value of t if it does, or explain why not if it does not.

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