Question

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

Answer 1

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=0-1+7=6
s(0)=-cos(0)-sin(0) + 7(0) + 3 =-1+0+0+3=2
All correct!