Question

for time t ≥ 0, the velocity of a particle moving along the x-axis is given by v(t) = sint, where t is measured in seconds and v(t) is in meters per second. the initial position of the particle at time t = 0 is x = 8. what is the total distance the particle traveled from time t = 0 to t = 2π?

Answer 1

By velocity function, the total distance is 8m.

We need to know about velocity to solve this problem. The velocity can be determined as

dV = dX / dT

dX = dV . dT

X = ∫dV . dT

where dV is velocity, dX is distance, dT is the time.

From the question above, we know that:

V(t) = sin(t) m/s

xo = 8 m

to = 0 s

t = 2π s

By substituting the parameters, we can determine the distance

X = ∫dV . dT

Integrate from t = 0 to 2π

X = ∫sin(t) . dT

X = [-cos(t)] + xo

the value of [-cos(t)] + xo from t = 0 to 2π is

X = [-cos(2π) - (-cos(0))] + 8

X = (-1 + 1) + 8

X = 8 m

For more on velocity at: brainly.com/question/25749514

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