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Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 3t2 + cos(t) and v(0) = 2?

Answer 1

Luke Alvarez

#v(t)=t^3+\sin t+2#

Given that the acceleration of an object as a function of time #t# as follows

#a=3t^2+\cost#

We know that the velocity #v# & acceleration #a# of an object are co-related as follows

#a=dv/dt#

#dv=adt#

#\int dv=\int a\ dt#

#v=\int (3t^2+\cost )\ dt#

#v=3(t^3/3)+\sin t+C#

#v=t^3+\sin t+C#

But given that at #t=0#, #v=2\ m/s# hence

#2=(0)^3+\sin (0)+C#

#C=2#

Now, the velocity #v(t)# of object at any time #t# is

#v(t)=t^3+\sin t+2#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.