Question
Asked Dec 12, 2019
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The acceleration of a car s after starting from rest is (75+10t-t2)/20 until the instant when this expression vanishes. After this instant the speed remains constant. 

A.Find the maximum acceleration

B. Time taken to attain the greatest speed

C.The greatest speed. 

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Expert Answer

Step 1

(A) The acceleration of the car is maximum, when its derivative is zero.

Write the expression for the expression for derivative of acceleration

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da dt d( 75 +10t – t? dt 20 10 – 2t = 0 20 t = 5 s

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Step 2

Substitute the value of time in the given acceleration expression

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75+10t – t? amax 20 /1=5s 75 +10(5 s) - (5) 20 = 4 m/s?

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Step 3

When the car attains a maximum speed, its acceleration is...

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a = 0 75 +10t – t? = 0 20 -10 + (10) – 4(-1)(75) 2(-1) =-5 s or 15 s

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Kinematics

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