Force acting on a particle of mass 2kg is given by F(t)=4t-8. Find the time when it comes to rest
Answers
ANS: (t = 6)
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after 4 secs body comes at rest if Force acting on a particle of mass 2kg is given by F(t)=4t-8.
Explanation:
F(t) = 4t - 8
F = ma
m = 2 kg
=> F = 2a
Equating Force
2a = 4t - 8
=> a = 2t - 4
a = dv/dt
=> dv = adt
=> dv = (2t - 4)dt
integrating on both sides
=> ∫ dv = ∫ (2t - 4)dt
=> v = t² - 4t + c
Assuming force applied on a body at rest
=> t = 0 v = 0
=> 0 = 0 - 0 + c
=> c = 0
=> v = t² - 4t
time when it comes to rest v = 0
=> t² - 4t = 0
=> t(t - 4) = 0
=> t = 0 or t = 4
after 4 secs body comes at rest
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