advanced integrals question,,, please help?

Question

if v(t)={3(t ^ 2), 0 =< t <= 2},{16 - 2t, 2 =< t <= 8) where v(t) is the velocity of a body after t seconds, t is time in seconds, find the displacement of the body from the start point when t is 5 seconds

ps: this is not a homework, and i really need the answer for my exam, and thanx in advance

Answer 1

Let first distance be Sa metres where :-
Sa = ∫ 3t² dt--------- between limits of 0 and 2
Sa = 3t³/3------limits 0 and 2
Sa = 8 m

Let second distance be Sb metres where:-
Sb = ∫ 16 - 2t dt-----limits 2 and 8
Sb = 16t - t²---------limits 2 and 8
Sb = (128 - 64) - (32 - 4)
Sb = 64 - 28 = 26 m

Distance = Sa + Sb = 34 m

Answer 2

Velocity is the time differential of displacement, so you will need to do definite integratation to get the displacement. Since your velocity function is in two parts then you will have to do two separate integrations. Be careful about the limits that you use in each definite integral. With this help try to finish it before looking at any detailed answer left here. Here's a hint to check that you have the right answer - it is a multiple of 5.

Follow up - you copy what is in the next answer at your peril! (Unless it is edited or deleted later.)