Instantaneous Acceleration in 2D Video Lessons

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Problem: An object has the following position vector: r(t) = (3m – (14 m/s3)t3)i + ((15 m/s)t + (0.5 m/s2)t2)j + (–2.4 m + (0.9 m/s)t) k. a) What is the velocity vector of the object?b) What is the acceleration vector of the object?c) At t = 7 s, what is the object’s distance from the origin?d) At t = 4 s, what is the x-component of the object’s velocity?e) At t = 2.5 s, what is the object’s speed?f) At t = 5.5 s, what is the object’s acceleration?

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Problem Details

An object has the following position vector: r(t) = (3m – (14 m/s3)t3)+ ((15 m/s)t + (0.5 m/s2)t2)j + (–2.4 m + (0.9 m/s)t) k

a) What is the velocity vector of the object?

b) What is the acceleration vector of the object?

c) At t = 7 s, what is the object’s distance from the origin?

d) At t = 4 s, what is the x-component of the object’s velocity?

e) At t = 2.5 s, what is the object’s speed?

f) At t = 5.5 s, what is the object’s acceleration?

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