Jake decided to walk from his room to the class 1.5 miles away. The class will s

Question

Jake decided to walk from his room to the class 1.5 miles away. The class will start in 14.0 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 3.8 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

given

d = 1.5 miles = 1.5*1.609*1000 = 2413.5 m

t = 14 min = 14*60 = 840 s

a = 3.8 mm/s^2 = 0.0038 m/s^2

distance travelled in 24 seconds = 0.5*a*t^2

= 0.5*0.0038*840^2

= 1340.6 m

so, he will be late.

let t' is the time taken

Apply,

d = 0.5*a*t'^2

==> t' = sqrt(2*d/a)

= sqrt(2*2413.5/0.0038)

= 1127 s

so he will be late by = 1127 - 840

= 287 s or 4.78 min

let a' is the required acceleration

apply, d = 0.5*a'*t^2

==> a' = 2*d/t^2

= 2*2413.5/840^2

= 0.0068 m/s^2 or 6.8 mm/s^2

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.