Question

Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) − sin(t) and v(0) = 3.

Answer 1

if a(t) = cos(t) − sin(t)
v(t) = sin(t) + cos(t) + c
given: v(0) = 0
3 = sin0 + cos0 + c
3 = 0 + 1 + c
c = 2

v(t) = sin(t) + cos(t) + 2