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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
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FindingTangentialand NormalComponents of Acceleration In Exercises 25-30, Find the tangential and normal components of acceleration at the given time t for the plane curve r(t).

r ( t ) = t 2 i + 2 t j , t = 1

To determine

To calculate: Tangential and normal components of acceleration at the time t=1 for the plane curve r(t)=t2i+2tj

Explanation

Given: r(t)=t2i+2tj,t=1

Formula used:

Tangential component of acceleration, aT=va|v|

Normal component of acceleration, aN=|v×a||v|

Calculation:

According to question:

The given plane curve is r(t)=t2i+2tj

The velocity, speed and acceleration for the given curve are given as:

v(t)=r'(t)=2t+2j|v(t)|=(2t)2+(2)2=4t2+4=2t2+1

a(t)=r"(t)=v'(t)=2i

Now calculate dot and cross product of velocity and acceleration:

va=(2ti+2j)(2i)=4t

v×a=(ijk2t20200)

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