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 1.5 m/s2 for 4 seconds. It then continues at a constant speed for 11.5 seconds, before getting tired and slowing down with constant acceleration coming to rest 91 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 2.8 seconds after it starts?

2)

3)

4)

5)

6)

Explanation / Answer

for hare

u = 0 m/s

a = 1.5 m/s^2

t = 4 s

v = u+ at

= 0 + 1.5 * 4

= 6 m/s

s1 = ut + 1/2(a*t^2)

= 0 + 1/2(1.5*16)

= 12 m

now he walks at a constant speed for 11.5 s

so s2 = 6*11.5 = 69

total distance so far = s1 + s2 = 12 + 69 = 81m

now u = 6

v = 0

s = 91 - 81 = 10m

v^2 = u^2 + 2as

so 0 = 36 - 20a

a= 36/20 = 1.8

v = u + at

0 = 6 - 1.8t

so t = 6/1.8 = 3.33 s

total time = 4 + 11.5 + 3.33 = 18.83 s

for tortoise

u = 0

s = 91

t = 18.83

s = ut + 1/2(at^2)

91 = 0 + 1/2(354.56a)

a = (91*2)/354.56

a = 0.51m/s^2

1)

u = 0;

a = 0.51

t = 2.8

so v = u+ at

v = 0+0.51*2.8

= 1.428 m/s^2

2)6m/s (see solution above)

3)81 m (see solution above)

4)1.8 n/s^2(see solution above)

5)18.83 s (see solution above)

6)0.51 m/s^2 (see solution above)

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