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

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

A	v(t) = sin(t) + cos(t) + 3
B	v(t) = sin(t) + cos(t) + 2
C	v(t) = sin(t) - cos(t) + 3
D	v(t) = sin(t) - cos(t) + 4

Answer 1

B is correct

v(0) = sin(0)+cos(0)+2 = 0+1+2 = 3

A has v(0)=0+1+3 = 4 which doesn't equal v(0)=3

C has v(0) =0-1+3 = 2 which doesn't equal v(0)=3

D does have v(0)=0-1+4=3 which does equal v(0)=3, but

a(t) = the derivative of v(t), the integral of sint-cost+4 = -cost+sint which does not = a(t)

only B has the integral of a(t) with the correct constant term =2 so that v(0)=3