math
posted by Kay .
Can you please check my work.
A particle is moving with the given data. Find the position of the particle.
a(t) = cos(t) + sin(t)
s(0) = 2
v(0) = 6
a(t) = cos(t) + sin(t)
v(t) = sin(t)  cos(t) + C
s(t) = cos(t)  sin(t) + Cx + D
6 = v(0) = sin(0) cos(0) + C
C=7
2= s(0) = cos(0)  sin(0) + 7 (0) + D
D= 3
s(t) = cos(t)  sin(t) + 7t + 3

All correct.
We can check backwards:
assume given:
s(t) = cos(t)  sin(t) + 7t + 3
v(t)=s'(t)=sin(t)cos(t)+7
a(t)=v'(t)=cos(t)+sin(t)
v(0)=sin(0)cos(0)+7=01+7=6
s(0)=cos(0)sin(0) + 7(0) + 3 =1+0+0+3=2
All correct!