A tortoise and hare start from rest and have a race. As the race begins, both accelerate forward. The hare accelerates uniformly at a rate of 0.9 m/s2 for 4.5 seconds. It then continues at a constant speed for 13.9 seconds, before getting tired and slowing down with constant acceleration coming to rest 74 meters from where it started. The tortoise accelerates uniformly for the entire distance, finally catching the hare just as the hare comes to a stop.
1) How fast is the hare going 2.7 seconds after it starts?
2) How fast is the hare going 9.2 seconds after it starts?
3) How far does the hare travel before it begins to slow down?
4) What is the acceleration of the hare once it begins to slow down?
5) What is the total time the hare is moving?
6) What is the acceleration of the tortoise?
A tortoise and hare start from rest and have a race. As the race begins, both accelerate forward. ?
2020-07-13 1:10 pm
回答 (2)
2020-07-13 2:53 pm
✔ 最佳答案
1) How fast (hV') is the hare going 2.7 seconds after it starts? hV' = a*t' = 0.9*2.7 = 2.43 m/sec 2) How fast (hV'') is the hare going 9.2 seconds after it starts?hV'' = a*t = 0.9*4.5= 4.05 m/sec 3) How far (d) does the hare travel before it begins to slow down?d = hV''*(13.9+t/2) = 4.05*(13.9+4.5/2) = 65.4 m 4) What is the acceleration a'' of the hare once it begins to slow down?a''= (0-hV''^2)/2d" = -16.40/148 = -0.111 m/sec^2 t'' = -hV''/a'' = 36.5 sec 5) What is the total time tt the hare is moving?tt = 4.5+13.9+36.5 = 54.9 sec 6) What is the acceleration a''' of the tortoise?
total distance td = 65.4+74 = 139.4 m
a''' = 2*td/tt^2 = 2*139.4 / 54.9^2 = 0.092 m/sec^2
tV = a'''*tt = 0.092*54.9 = 5.075 m/sec
2020-07-13 2:07 pm
1)
vₒ = 0 m/s, t = 2.7 s, a = 0.9 m/s²
s = vₒt + (1/2)at²
s = 0 + (1/2)(0.9)× 2.7²
Distance traveled by the hare, s = 3.3 m
====
2)
For the first 4.5 s:
vₒ = 0 m/s, t = 4.5 s, a = 0.9 m/s²
v = u + at
v = 0 + 0.9 × 4.5
Final velocity, v = 4.05 m/s
Speed at 9.2 s after the hare starts = 4.05 m/s
====
3)
For the first 4.5 s:
vₒ = 0 m/s, t = 4.5 s, a = 0.9 m/s²
s = vₒt + (1/2)at²
s = 0 + (1/2)(0.9)× 4.5²
s = 9.1 m
Before the hare begins to slow down, distance traveled
= 9.1 + 4.05 × 13.9
= 65.4 m
====
4)
Consider the journey when the hare slows down:
vₒ = 4.05 m/s, s = (74 - 65.4) m, v = 0 m/s
v² = vₒ² + 2as
0 = 4.05² + 2a(74 - 65.4)
Acceleration, a = -0.95 m/s²
====
5)
Consider the journey when the hare slows down:
vₒ = 4.05 m/s, s = (74 - 65.4) m, v = 0 m/s
s = [(vₒ + v)/2]t
74 - 65.4 = [(4.05 + 0)/2]t
Time taken = 4.2 s
Total time taken when the hare is moving = 4.5 + 13.9 + 4.2 = 22.6 s
====
6)
Consider the tortoise:
t = 22.6 s, vₒ = 0 m/s, s = 74 m
s = vₒt + (1/2)at²
74 = 0 + (1/2)a(22.6)²
Acceleration, a = 0.29 m/s
vₒ = 0 m/s, t = 2.7 s, a = 0.9 m/s²
s = vₒt + (1/2)at²
s = 0 + (1/2)(0.9)× 2.7²
Distance traveled by the hare, s = 3.3 m
====
2)
For the first 4.5 s:
vₒ = 0 m/s, t = 4.5 s, a = 0.9 m/s²
v = u + at
v = 0 + 0.9 × 4.5
Final velocity, v = 4.05 m/s
Speed at 9.2 s after the hare starts = 4.05 m/s
====
3)
For the first 4.5 s:
vₒ = 0 m/s, t = 4.5 s, a = 0.9 m/s²
s = vₒt + (1/2)at²
s = 0 + (1/2)(0.9)× 4.5²
s = 9.1 m
Before the hare begins to slow down, distance traveled
= 9.1 + 4.05 × 13.9
= 65.4 m
====
4)
Consider the journey when the hare slows down:
vₒ = 4.05 m/s, s = (74 - 65.4) m, v = 0 m/s
v² = vₒ² + 2as
0 = 4.05² + 2a(74 - 65.4)
Acceleration, a = -0.95 m/s²
====
5)
Consider the journey when the hare slows down:
vₒ = 4.05 m/s, s = (74 - 65.4) m, v = 0 m/s
s = [(vₒ + v)/2]t
74 - 65.4 = [(4.05 + 0)/2]t
Time taken = 4.2 s
Total time taken when the hare is moving = 4.5 + 13.9 + 4.2 = 22.6 s
====
6)
Consider the tortoise:
t = 22.6 s, vₒ = 0 m/s, s = 74 m
s = vₒt + (1/2)at²
74 = 0 + (1/2)a(22.6)²
Acceleration, a = 0.29 m/s
收錄日期: 2021-04-18 18:33:48
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20200713051046AAjqnKZ