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^{2}+tlnt gives the position from time [1,e] find:

**a**. the velocity at time t

**b**. the acceleration at time t

**c**. describe the motion of the object: when is it moving forward or moving backward. also compute the total distance traveled during the interval

**d**. when is the object accelerating and when is it decellerating

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my work

s(t)=t

^{2}+tlnt

v(t)=2t+1+lnt

a(t)=2+(1/t)

Part a answer. v(t)=2(t)+1+lnt

part b answer a(t)=2+(1/t)

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Are my answers for a and b correct? And how would I find parts c and d.

Thank you!