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

Q1:

A racehorse passing through a starting gate accelerates from rest to a velocity of 15.0 m/s due west in a time interval of 1.80 s. Find the racehorse’s average acceleration. Assume that east corresponds to positive displacement.

Q2:

A particle that is in motion has a changing velocity that is modeled by the function 𝑣 ( 𝑡 ) = 2 0 𝑡 − 5 . 0 𝑡 2 m/s.

Find the instantaneous velocity of the particle at 𝑡 = 1 . 0 s .

Find the instantaneous velocity of the particle at 𝑡 = 2 . 0 s .

Find the instantaneous velocity of the particle at 𝑡 = 3 . 0 s .

Find the instantaneous velocity of the particle at 𝑡 = 5 . 0 s .

Find the instantaneous acceleration of the particle at 𝑡 = 1 . 0 s .

Find the instantaneous acceleration of the particle at 𝑡 = 2 . 0 s .

Find the instantaneous acceleration of the particle at 𝑡 = 3 . 0 s .

Find the instantaneous acceleration of the particle at 𝑡 = 5 . 0 s .

Q3:

A sprinter runs a 100-m race in 9.74 s. The sprinter accelerated for 3.22 s to reach her maximum speed, which she maintained for the rest of the race.

Find the sprinter’s acceleration.

Find the sprinter’s maximum speed.

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