A particle is moving with the given data. Find the position of the particle.
v(t) = sin(t) minus cos(t), s(0) = 3
a.
s(t) = 4 minus cos(t) minus sin(t)
b.
s(t) = cos^2(t)
c.
s(t) = 1 minus t minus sin(t)
d.
s(t) = cos(t) minus sin(t)
e.
s(t) = 1 minus cos(t) + sin(t)
To find the position of the particle, we need to integrate the velocity function v(t) with respect to time to get the position function s(t) and then apply the initial condition s(0) = 3.
Given v(t) = sin(t) - cos(t), we need to integrate this function to find s(t):
∫(sin(t) - cos(t)) dt = -cos(t) - sin(t) + C
Applying the initial condition s(0) = 3:
s(0) = -cos(0) - sin(0) + C = -1 - 0 + C = 3
C = 4
Therefore, the position function is s(t) = -cos(t) - sin(t) + 4.
The correct answer is:
a. s(t) = 4 - cos(t) - sin(t)