A tortoise and hare start from rest and have a race. As the race begins, both ac
ID: 2271315 • Letter: A
Question
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 1.4 m/s2 for 4.9 seconds. It then continues at a constant speed for 11.3 seconds, before getting tired and slowing down with constant acceleration coming to rest 107 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 10.7 seconds after it starts? ______________m/s
2) How far does the hare travel before it begins to slow down? _______________m
3) What is the acceleration of the hare once it begins to slow down? ________________m/s^2
4) What is the total time the hare is moving? ________________s
5) What is the acceleration of the tortoise? _________________m/s^2
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 1.4 m/s2 for 4.9 seconds. It then continues at a constant speed for 11.3 seconds, before getting tired and slowing down with constant acceleration coming to rest 107 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. How fast is the hare going 10.7 seconds after it starts? ______________m/s How far does the hare travel before it begins to slow down? _______________m What is the acceleration of the hare once it begins to slow down? ________________m/s^2 What is the total time the hare is moving? ________________s What is the acceleration of the tortoise? _________________m/s^2Explanation / Answer
1) v = u + a*t = 0 + 1.4*4.9 = 6.86 m/s
2) s = 0.5*1.4*4.9^2 + (1.4*4.9)*11.3 = 94.33 m
3) v2^2 - v1^2 = 2*a*(107-94.33)
0 - 6.86^2 = 2*a*12.67
a = -47.06/(2*12.67)
= -1.86 m/s^2
4) let t is the time taken to slow down
v2 = v1 + a*t
t = -v1/a = -6.86/-1.86= 3.7 s
total time = 4.9+11.3+3.7 = 19.9 s
5)s = 0.5*a*t^2
107 = 0.5*a*19.9^2
a = 2*107/19.9^2 = 0.54 m/s^2
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