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A) Acceleration is the rate of change of velocity with respect to time; therefore, in order to calculate it we need to differentiate the given equation of velocity v with respect to time t: a = dv / dt = ...

For this question the FOIL method can be used. FOIL stands for first, outside, inside, and last, and is used to make sure each term is multiplied by each other term. Firstly, multiply the first terms of e...

The chain rule needs to be applied when you are differentiating a function f of x with respect to a variable t, x is a function of (i.e. given f(x) and x(t), you want to calculate df/dt. 

To do so ...

*Use identity sinxcosx = 1/2sin2x

=5/2sin2x + 5cosx

*then use simple integration gives

=(-5/2 x1/2)cosx + 5sinx + c

= =5/4cosx +5sinx + c

5 + 5√ 2 - √ 8 - √ 16    (Break up all terms in terms of square roots of 2)

5 + 5√ 2 - √ 8 - 4

5 + 5√ 2 - 2 √ 2 - 4 

1 + 3√2