A particle is moving as given by the data below
4sin(t)-3cos(t); s(0)=0
s(t) = -5cos(t)-3sin(t)+5
hope this helps
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To find the position function for the particle given its velocity function and initial condition, we need to integrate the velocity function with respect to time.
Given that the velocity function is 4sin(t) - 3cos(t), we integrate it to get the position function.
∫ (4sin(t) - 3cos(t)) dt = -4cos(t) - 3sin(t) + C
Here, C is the constant of integration.
Since we are given that s(0) = 0, we can solve for C.
0 = -4cos(0) - 3sin(0) + C
0 = -4(1) - 3(0) + C
0 = -4 + C
C = 4
Therefore, the position function of the particle is:
s(t) = -4cos(t) - 3sin(t) + 4