Find the particles displacementfor the given interval, if s(0)=3, what is the particles final position?

Question

v(t)=5cos(t) 0=

find the total distance traveled y the particle

Answer 1

integrating v(t), we get

s(t) = 5 sin(t) + C ,
substituting s(0)=3, we get C=3
therefore
s(t) = 5 sint(t) + 3
Substituting in the above eqn, the final position at t = 2 pi is again 3

Answer 2

Given the velocity is d/ds ds/dt then the position is simply the integral of the velocity or
s(t) = s(0) + 5sin(t) If s(0) = 3, then at t = 2π s(t) = 3

HTH ☺


Doug

Answer 3

x(t) = 5sin(t) + 3
x(2π) = 3
2π
∫(5sin(t) + 3)dt = -5 + 5 + 6π - 0 = 6π
0

Answer 4

Missionary.