Jake decided to walk from his room to the class 1.3 miles away. The class will s

Question

Jake decided to walk from his room to the class 1.3 miles away. The class will start in 14.1 minutes. As he is walking, he is getting more and more concerned about making it on time. So he keeps walking ever a little faster, maintaining a tiny acceleration of 3.6 mm/s2. Is he going to be late after all? If you find that he will be late, answer by how many minutes. Perhaps he will arrive early? Then he did not need to exert himself quite so much! In this case, what is the smallest magnitude of acceleration that would still get him to class in time (the answer may be in either mm/s2, or in m/s2).

Explanation / Answer

distance = 1.3 miles = 2092.15 m

if time taken >14.1 minutes(846 seconds ), then he is late

acceleration = 3.6mm/s^2 = 3.6/1000 m/s^2 = 0.0036m/s^2

distance travlled with this acceleration in 846 seconds = 1/2 a t^2

= 1/2 (0.0036) (846)^2 = 1288 m

So he is able to reach only 1288 m in 846s(14.1 minutes) and is short by 803metres (2092-1288)  

he will travel 803 metres in

803 = 1/2 (0.0036) t^2 ;

t = 668 seconds = 11 minutes

so he is late by 11 minutes

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