world class speed skaters can skate a 3,000 meter course in about 4 minutes. what is their average speed for this course?
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Ответ:
12.5 m/s.
v = d/t
(60 s/1 min)*(4 min) = 240 s
v = 3000 m/240 s
v = 12.5 m/s
Ответ:
(a) 52.724 m/s
(b) Total displacement, d = 551.25 m
Solution:
As per the question:
Initial acceleration of the speed boat, a = - 2.01![m/s^{2}](/tpl/images/0267/0872/7d0a1.png)
Time duration, t = 7.00 s
Additional time, t' =6.00 s
Acceleration for additional time, a' = 0.518![m/s^{2}](/tpl/images/0267/0872/7d0a1.png)
The followed up acceleration, a'' = 1.49![m/s^{2}](/tpl/images/0267/0872/7d0a1.png)
Time duration, t'' = 8.00 s
(a) Now, to calculate the velocity of the boat at timer, t = 21.0 s, we have:
After the initial 7.00 s, the velocity of the boat, from eqn-1 of motion:
v = u + at
v = 0 - 2.1(7.00) = - 14.7 m/s
After t + t' = 13 s:
v' = v + at
v' = 14.7 + 0.518(13) = 21.434 m/s
Now, velocity of the boat after t = 21 s:
v'' = v' + a''t
v'' = 21.434 + 1.49(21) = 52.724 m/s
(b) Now, the total displacement, d:
For the first case:
d = ut +![\frac{1}{2}at^{2} = 0 - 0.5\times 2.1\times 7^{2} = - 51.45 m](/tpl/images/0267/0872/48652.png)
For the second case:
d = v't' = 21.434(6) = 128.6 m
For the third case:
d = ut +![\frac{1}{2}a't'^{2} = 0 + 0.5\times 0.518\times 6^{2} = 4.65 m](/tpl/images/0267/0872/8148d.png)
For the fourth case:
d = v''t'' = 52.724(8) = 421.79 m
For the last case:
d = ut +![\frac{1}{2}a't'^{2} = 0 + 0.5\times 1.49\times 8^{2} = 47.68 m](/tpl/images/0267/0872/5150f.png)
Total displacement, d = -51.45 + 128.6 + 4.65 + 421.79 + 47.68 = 551.25 m