Final answer:
The velocity of a particle with the motion equation s = t^(-1) - t at t = 5 seconds is -25 m/s, indicating a reversal in direction as it decreases to zero velocity between 3 to 5 seconds and then becomes negative.
Step-by-step explanation:
The question pertains to the motion of a particle moving along a straight line with a specific equation of motion. When given that the equation of motion is s = f(t) = t^(-1) - t, where s is the displacement in meters and t is the time in seconds, we can find the velocity by differentiating the position function with respect to time. The speed is the absolute value of the velocity.
To find the velocity at t = 5 seconds, we calculate the derivative of f(t), which yields v(t) = -t^(-2) - 1. Substituting t = 5 into this expression, we get v(5 s) = -25 m/s. Between t = 3 s and t = 5 s, the particle reduces its velocity to zero and then becomes negative, indicating a reversal in direction, and now is speeding up again in the opposite direction.
For this problem, the acceleration can typically be found by differentiating the velocity function. Commonly, acceleration gives us information on how quickly the velocity is changing over time.