Final answer:
To determine the body's motion, we plug values into the provided function.
a. When t is 2 seconds, the displacement is 0 m, meaning no distance moved from the origin.
b. The average velocity during the 3rd second is -6 m/s,
c. which is -21.6 km/hr when converted.
Step-by-step explanation:
The question is about a body moving along the x-axis and its motion described by the displacement function s(t) = 4t - 2t^2.
- a. Distance moved when t is 2 seconds: The body's position at t=2 can be found by plugging t=2 into the displacement function: s(2) = 4(2) - 2(2)2 = 8 - 8 = 0. Since the particle returns to the origin, the distance moved is the absolute value of the total displacement from t=0 to t=2, which is also 0, as the body has returned to the starting position.
- b. Average velocity during the 3rd second: This is found by calculating the change in position from t=2 to t=3, and dividing by the change in time (1 second). The body's position at t=2 is s(2) = 0 and at t=3 is s(3) = 4(3) - 2(3)2 = 12 - 18 = -6. So, average velocity = (-6 - 0) / (3 - 2) = -6 m/s.
- c. Average velocity in km/hr during the 3rd second: To convert -6 m/s to km/hr multiply by 3.6. So, the average velocity is -6 * 3.6 = -21.6 km/hr.