A tortoise and hare start from rest and have a race. As the race begins, both ac

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 1.1 m/s2 for 4.1 seconds. It then continues at a constant speed for 13.6 seconds, before getting tired and slowing down with constant acceleration coming to rest 81 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 2.9 seconds after it starts?

2)

How fast is the hare going 7.1 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?

See solution

)

What is the acceleration of the tortoise?

Explanation / Answer

(1)
Initial Velocity of hare = 0
Final Velocity , v = ?
Acceleration, a = 1.1 m/s^2
t = 2.9 s

v = u + a*t
v = 0 + 1.1 * 2.9 m/s
v = 3.19 m/s

Speed of hare after 2.9 s, v = 3.19 m/s

(2)
Speed of hare @ 7.1 s = Speed of hare after 4.1 s, because it starts moving with constant speed after intial acceleration.

nitial Velocity of hare = 0
Final Velocity , v = ?
Acceleration, a = 1.1 m/s^2
t = 4.1 s

v = u + a*t
v = 0 + 1.1 * 4.1 m/s
v = 4.51 m/s
Speed of hare after 7.1 s before it begins, v = 4.51 m/s

(3)
Initial Velocity of hare = 0
Acceleration, a = 1.1 m/s^2
t1 = 4.1 s
t2 = 13.6 s
v = 4.51 m/s

Distance travelled by hare before it begins to slow down,
S = u*t2 + 1/2 * at2^2 + v*t2
S = 0 + 1/2 * 1.1 * 4.1^2 + 13.6 * 4.51 m
S =  70.58 m

Distance travelled by hare before it begins to slow down, S =  70.58 m

(4)
Inital Speed = 4.51 m/s
Final Speed = 0
Distance travelled before hare comes to stops = 81 - 70.58 = 10.42 m

v^2 = u^2 - 2*a*s
0 = 4.51^2 - 2*a*10.42
a = 0.976 m/s^2
Acceleration  of the hare once it begins to slow down,a = 0.976 m/s^2

(5)
V = u + a*t
0 = 4.51 - 0.976 * t
t =

Total time hare is moving, t = 4.1 s + 13.6 s + 4.62 s
Total time hare is moving, t = 22.32 s

(6)
Initial Velocity, u = 0
Distance, s = 81 m
time, t = 22.32 s

s = u*t + 1/2 * at^2
81 = 0 + 1/2 * a * 22.32^2
a = 0.325 m/s^2
Acceleration of the tortoise, a = 0.325 m/s^2

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