a(t)=cos t-sin t
dv/dt=cos t-sin t
integrating,
v(t)=sin t+cos t +c
where c is a constant
now a t=0,
v=1
so c=0
v(t)=sin t+cos t
dx/dt=sin t+cos t
x(t)=-cos t+sin t+c
x(0)=0
so c-1=0
c=1
hence x(t)=sin t-cos t+1
b)v(t)=sin t+cos t
v(t)=0
==> sin t=-cos t
tan t=-1
t=-pi/4 or 3*pi/4
c)x(t)=sin t-cos t+1
plotting it for t=[0,5] we can see that
minimum occurs t at=5 and maximum occurs at dx/dt=0
i.e. t=3*pi/4=2.356 seconds
minimum value=-0.24259
maximum value=2.4142
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