Answer:
V(3) =14i^ -34j^ +8.57 k^
S(3) =(25,-45,3.97)
Step-by-step explanation:
We know that
V =a dt
from t=0 to 3s
V = 4i - 6tJ + sin(.2t)k m/s² dt
V =4t i^ - 3t^2j^ - cos(2t)/2 k^ +C
So we have
V(0) =-1/2 k^ +C =2i -7j +8.4 k
C=2i -7j +8.9k^
V =4t i^ - 3t^2j^ - cos(2t)/2 k^ + 2i -7j +8.9k^
Then putting 3s
V(3) =14i^ -34j^ +8.57 k^
Also
S(t) =V(t) dt
S(t) = 4t i^ - 3t^2j^ - cos(2t)/2 k^ + 2i -7j +8.9k^] dt
S(t)= (2t^2 +2t)i^ - (t^3 +7t) j^ -[sin(2t)/4 - 8.9t] k^ +C =i+3j-5k
So at t= 0 we have
S(0) = C= i+3j-5k
So S(t) =(2t^2 +2t)i^ - (t^3 +7t) j^ -[sin(2t)/4 - 8.9t] k^ +i+3j-5k
When t= 3
S(3) =25i -45j + 3.97k
S(3) =(25,-45,3.97)