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Answer :
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Final answer:
The average speed between t = 1.70 s and t = 3.00 s is 0 m/s. The instantaneous speed at t = 1.70 s is 3.752 m/s. The average acceleration between t = 1.70 s and t = 3.00 s is 0 m/s². The instantaneous acceleration at t = 1.70 s is 0 m/s². The object is at rest at t = 2.00 s.
Explanation:
Motion along the x-axis
In physics, motion along the x-axis refers to the movement of an object in a straight line horizontally. The equation x = 2.752 - 2.00 +3.00 represents the position of the object at different times.
(a) Average Speed
The average speed between t = 1.70 s and t = 3.00 s can be calculated by finding the total distance traveled and dividing it by the total time taken.
To find the total distance traveled, we need to find the difference in position between t = 1.70 s and t = 3.00 s.
Substituting the values of t into the equation x = 2.752 - 2.00 +3.00, we get:
x(1.70) = 2.752 - 2.00 +3.00 = 3.752 m
x(3.00) = 2.752 - 2.00 +3.00 = 3.752 m
The total distance traveled is the difference between these two positions:
Total distance = x(3.00) - x(1.70) = 3.752 m - 3.752 m = 0 m
The total time taken is the difference between t = 3.00 s and t = 1.70 s:
Total time = 3.00 s - 1.70 s = 1.30 s
Now, we can calculate the average speed:
Average speed = Total distance / Total time = 0 m / 1.30 s = 0 m/s
(b) Instantaneous Speed
The instantaneous speed at t = 1.70 s can be found by substituting the value of t into the equation x = 2.752 - 2.00 +3.00:
x(1.70) = 2.752 - 2.00 +3.00 = 3.752 m
Therefore, the instantaneous speed at t = 1.70 s is 3.752 m/s.
(c) Average Acceleration
The average acceleration between t = 1.70 s and t = 3.00 s can be calculated by finding the change in velocity and dividing it by the change in time.
To find the change in velocity, we need to find the difference in position between t = 1.70 s and t = 3.00 s.
Substituting the values of t into the equation x = 2.752 - 2.00 +3.00, we get:
x(1.70) = 2.752 - 2.00 +3.00 = 3.752 m
x(3.00) = 2.752 - 2.00 +3.00 = 3.752 m
The change in velocity is the difference between these two positions:
Change in velocity = x(3.00) - x(1.70) = 3.752 m/s - 3.752 m/s = 0 m/s
The change in time is the difference between t = 3.00 s and t = 1.70 s:
Change in time = 3.00 s - 1.70 s = 1.30 s
Now, we can calculate the average acceleration:
Average acceleration = Change in velocity / Change in time = 0 m/s / 1.30 s = 0 m/s²
(d) Instantaneous Acceleration
The instantaneous acceleration at t = 1.70 s can be found by substituting the value of t into the equation x = 2.752 - 2.00 +3.00:
x(1.70) = 2.752 - 2.00 +3.00 = 3.752 m
Therefore, the instantaneous acceleration at t = 1.70 s is 0 m/s².
(e) Object at Rest
The object is at rest when its velocity is zero. From the given equation x = 2.752 - 2.00 +3.00, we can see that the object is at rest when x = 0. Therefore, we need to solve the equation for x = 0:
0 = 2.752 - 2.00 +3.00
Simplifying the equation, we get:
2.752 - 2.00 +3.00 = 0
Therefore, the object is at rest at t = 2.00 s.
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