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In this lesson, we will learn how to calculate instantaneous velocity as the rate of displacement change in a time interval that approaches zero.

Q1:

A particle moves along the 𝑥 -axis according to 𝑥 ( 𝑡 ) = 1 0 𝑡 − 2 𝑡 2 m .

What is the instantaneous velocity at 𝑡 = 2 s ?

What is the instantaneous velocity at 𝑡 = 3 s ?

What is the instantaneous speed at 𝑡 = 2 s ?

What is the instantaneous speed at 𝑡 = 3 s ?

What is the average velocity between 𝑡 = 2 s and 𝑡 = 3 s ?

Q2:

The position of a particle varies according to 𝑥 ( 𝑡 ) = 3 . 0 𝑡 − 3 . 0 𝑡 2 m.

What is the particle’s instantaneous velocity when 𝑡 = 0 . 2 5 s ?

What is the particle’s instantaneous velocity when 𝑡 = 0 . 5 0 s ?

What is the particle’s instantaneous velocity when 𝑡 = 1 . 0 s ?

What is the particle’s instantaneous speed when 𝑡 = 0 . 2 5 s ?

What is the particle’s instantaneous speed when 𝑡 = 0 . 5 0 s ?

What is the particle’s instantaneous speed when 𝑡 = 1 . 0 s ?

Q3:

What quanity is displacement the integral of?

Q4:

The position of an object changes as a function of time according to 𝑥 ( 𝑡 ) = − 3 𝑡 2 m.

What is the object’s velocity when 𝑡 = 1 s?

What is the object’s speed when 𝑡 = 1 s?

Q5:

A particle’s position varies according to 𝑥 ( 𝑡 ) = 3 . 0 𝑡 + 0 . 5 0 𝑡 2 3 m.

What is the particle’s instantaneous velocity when 𝑡 = 2 . 0 s?

What is the particle’s average velocity between 𝑡 = 1 . 0 s and 𝑡 = 3 . 0 s?

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