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Answer :
Final answer:
To calculate the displacement of the curling stone, the time taken to come to rest was first found using the equation of motion, then the total displacement was calculated with the displacement formula resulting in a total displacement of 28.521 meters.
Explanation:
Calculating the Displacement of a Curling Stone
To determine the total displacement of the curling stone, we can use the equations of motion. The initial velocity (v_i) is given as 1.69 meters per second, and the constant acceleration (a) is -0.05 m/s² (negative because it is slowing down). We also know that the final velocity (v_f) is 0 m/s when the stone comes to rest.
Using the equation v_f = v_i + at, where t is the time, we can find the time it takes for the stone to come to rest:
v_f = v_i + at
0 = 1.69 + (-0.05)t
t = 1.69 / 0.05
t = 33.8 seconds
Now, we can calculate the total displacement (s) using the equation s = v_i*t + 0.5*a*t²:
s = (1.69 m/s * 33.8 s) + 0.5 * (-0.05 m/s²) * (33.8 s)²
s = 57.082 + 0.5 * (-0.05) * 1142.44
s = 57.082 - 28.561
s = 28.521 meters
The total displacement of the curling stone before it comes to rest is 28.521 meters.
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