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 1.3 m/st for 4.5 seconds. It then continues at a constant speed for 12.3 seconds, before and slowing down with constant acceleration coming to rest 96 meters from started. The tortoise accelerates unfformly for the entire distance, finally catching the hare just as the hare comes to a stop. tired 1) How fast is the hare going 1.3 seconds after it starts? See solution Your submiss 3.12 Computed value: 3.12 Feedback: Submitted: Wednesday, September 5 at 3:43 PM 2) How fast is the hare going 8.2 seconds after it starts? See solution m/s sue 3) How far does the hare travel before it begins to slow down? See solution m so 4) What is the acceleration of the hare once it begins to slow down? See solution m/s somit 5) What is the total time the hare is moving? See solution 6) What is the acceleration of the tortoise? See solution (Survey Question)

Explanation / Answer

(1) vf = vi + a t

v = 0 + (1.3)(1.3) = 1.69 m/s

(2) v = 0 + (1.3 x 4.5)

v = 5.85 m/s

(3) during acceleration,

d1 = vi t + a t^2 /2 = 0 + (1.3 x 4.5^2 /2 ) = 13.2 m

when it travel with constant speed,

d2 = (5.85)(12.3) = 71.955 m

d = d1 + d2 = 85.2 m

(4) distance travelled during deceleration

d = 96 - 85.2 = 10.8 m

vf^2 - vi^2 = 2 a d

0^2 - 5.85^2 = 2(a)(10.8)

a = - 1.58 m/s^2

(5) 0 = 5.85 - 1.58 t3

t3 = 3.71 s

t = 4.5 + 12.3 + 3.71 = 20.5 s

(6) d =vi t + a t^2 / 2

96 = 0 + a(20.5^2)/2

a = 0.46 m/s^2

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