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Differentiation Question Help (1 Viewer)

202025

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A body starts from rest and moves in a straight line so that its velocity v ms^-1 after t seconds is given by v = 2t + 6t^2. Calculate:

(a) its acceleration at the end of the first second

(b) its displacement after 5 seconds, given that the body is initially at zero displacement.

I have solved (a), however I am struggling with (b)


note: This question is from the differentiation chapter in my textbook therefore I believe that a method other than integration should be used.
 

HoldingOn

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I think they want you to use integration hence they have specified an initial condition for the body's displacement- indicating that the constant is zero. Also note that the acceleration is not uniform as the velocity function forms a parabola- so we can't use shape formulas like area of a triangle.
 
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202025

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This question is from Chapter 7 - Calculus - Introduction to Differentiation; from the textbook New Senior Mathematics Advanced Year 11&12, Third Edition. Primitive functions are not introduced until Chapter 16 - The anti-derivative.
 

HoldingOn

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This question is from Chapter 7 - Calculus - Introduction to Differentiation; from the textbook New Senior Mathematics Advanced Year 11&12, Third Edition. Primitive functions are not introduced until Chapter 16 - The anti-derivative.
The only way I can see how to do it without integration is taking the average velocity and then multiplying by the time. But this would only give you an approximation.
 
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