Answer:
1.
Given:
Initial velocity (u) = 20.0 m/s, east
Acceleration (a) = 3.2 m/s2
Time (t) = 5.0 s
Unknown:
Displacement (s)
Formula:
s = ut + 1/2at^2
Solution:
s = (20.0 m/s)(5.0 s) + 1/2(3.2 m/s2)(5.0 s)^2
s = 100.0 m + 1/2(3.2 m/s2)(25 s2)
s = 100.0 m + 40.0 m
s = 140 m, east
Answer: The displacement of the car is 140m, east.
2.
Initial velocity (u) = 6.0 m/s, north
Final velocity (v) = 8.0 m/s, north
Acceleration (a) = 0.5 m/s*2, north
Distance (s)
v^2 = u^2 + 2as
s = (v^2 - u^2) / 2a
s = [(8.0 m/s)^2 - (6.0 m/s)^2] / 2(0.5 m/s*2)
s = (64 m^2/s^2 - 36 m^2/s^2) / 1 m/s^2
s = 28 m
Answer: The distance the boat travels is 28m.
3.
Initial velocity (u) = 350 m/s, east
Time (t) = 0.0050 s
Final velocity (v) = 0 m/s
Acceleration (a)
a = (v - u) / t
a = (0 m/s - 350 m/s) / 0.0050 s
a = -70,000 m/s^2
Answer: The acceleration of the dart is -70,000m/(s^2).
4.
Initial velocity (u) = 0 m/s
Displacement (s) = 17 m, east
Time (t) = 3.8 s
Final velocity (v)
v = u + at
Using s = ut + 1/2at^2, we can solve for acceleration:
17 m = 0 m/s * 3.8 s + 1/2a(3.8 s)^2
17 m = 7.22a
a = 2.35 m/s^2
Using v = u + at, we can now solve for final velocity:
v = 0 m/s + (2.35 m/s^2)(3.8 s)
v = 8.9 m/s, east
Answer: Her final velocity is 8.9 m/s, east.
5.
Initial velocity (u) = 15 m/s, west
Acceleration (a) = 7 m/s*2, east
Time (t) = 4.0 s
v = 15 m/s + (7 m/s*2)(4.0 s)
v = 43 m/s, east
Answer: The helicopter's final velocity is 43m/s east.
Explanation:
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Answers & Comments
Answer:
1.
Given:
Initial velocity (u) = 20.0 m/s, east
Acceleration (a) = 3.2 m/s2
Time (t) = 5.0 s
Unknown:
Displacement (s)
Formula:
s = ut + 1/2at^2
Solution:
s = (20.0 m/s)(5.0 s) + 1/2(3.2 m/s2)(5.0 s)^2
s = 100.0 m + 1/2(3.2 m/s2)(25 s2)
s = 100.0 m + 40.0 m
s = 140 m, east
Answer: The displacement of the car is 140m, east.
2.
Given:
Initial velocity (u) = 6.0 m/s, north
Final velocity (v) = 8.0 m/s, north
Acceleration (a) = 0.5 m/s*2, north
Unknown:
Distance (s)
Formula:
v^2 = u^2 + 2as
Solution:
s = (v^2 - u^2) / 2a
s = [(8.0 m/s)^2 - (6.0 m/s)^2] / 2(0.5 m/s*2)
s = (64 m^2/s^2 - 36 m^2/s^2) / 1 m/s^2
s = 28 m
Answer: The distance the boat travels is 28m.
3.
Given:
Initial velocity (u) = 350 m/s, east
Time (t) = 0.0050 s
Final velocity (v) = 0 m/s
Unknown:
Acceleration (a)
Formula:
a = (v - u) / t
Solution:
a = (0 m/s - 350 m/s) / 0.0050 s
a = -70,000 m/s^2
Answer: The acceleration of the dart is -70,000m/(s^2).
4.
Given:
Initial velocity (u) = 0 m/s
Displacement (s) = 17 m, east
Time (t) = 3.8 s
Unknown:
Final velocity (v)
Formula:
s = ut + 1/2at^2
v = u + at
Solution:
Using s = ut + 1/2at^2, we can solve for acceleration:
s = ut + 1/2at^2
17 m = 0 m/s * 3.8 s + 1/2a(3.8 s)^2
17 m = 7.22a
a = 2.35 m/s^2
Using v = u + at, we can now solve for final velocity:
v = u + at
v = 0 m/s + (2.35 m/s^2)(3.8 s)
v = 8.9 m/s, east
Answer: Her final velocity is 8.9 m/s, east.
5.
Given:
Initial velocity (u) = 15 m/s, west
Acceleration (a) = 7 m/s*2, east
Time (t) = 4.0 s
Unknown:
Final velocity (v)
Formula:
v = u + at
Solution:
v = u + at
v = 15 m/s + (7 m/s*2)(4.0 s)
v = 43 m/s, east
Answer: The helicopter's final velocity is 43m/s east.
Explanation:
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