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Answer :
Final answer:
To find the average speed, displacement, instantaneous speed, average acceleration, instantaneous acceleration, and the time at which the object is at rest for a given position function.
Explanation:
To determine the average speed between t=1.70 s and t=3.20 s, we need to find the distance traveled and divide it by the time. We can do this by subtracting the initial position from the final position. The distance traveled is the absolute value of the difference in positions. In this case, the displacement is equal to the distance traveled because the object moves along a straight line and does not change direction. The average speed is calculated by dividing the distance traveled by the time interval.
To find the instantaneous speed at t=1.70 s and t=3.20 s, we need to take the derivative of the position function with respect to time. The derivative gives us the rate of change of position with respect to time, which represents the velocity. To find the instantaneous speed, we take the absolute value of the velocity. The average velocity between 0 and t=1.70 s is obtained by dividing the position at t=1.70 s by the time interval, and the average velocity between 0 and t=3.20 s is obtained by dividing the position at t=3.20 s by the time interval.
To determine the average acceleration between t=1.70 s and t=3.20 s, we need to find the change in velocity and divide it by the time interval. The change in velocity is the difference in velocities. The average acceleration is calculated by dividing the change in velocity by the time interval.
The instantaneous acceleration at t=1.70 s and t=3.20 s can be obtained by taking the derivative of the velocity function with respect to time. The derivative gives us the rate of change of velocity with respect to time, which represents the acceleration.
An object is at rest when its velocity is zero. To find the time at which the object is at rest, we need to solve the velocity function for t when the velocity is equal to zero.
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