SOLUTION: A point moves in a straight line such that its acceleration a is given by a=2(4-t)^1/2, 0≤t≤4. If it starts at rest, find an expreesion fot the velocity v where a =dv/d

Algebra ->  Equations -> SOLUTION: A point moves in a straight line such that its acceleration a is given by a=2(4-t)^1/2, 0≤t≤4. If it starts at rest, find an expreesion fot the velocity v where a =dv/d      Log On


   

Question 430896: A point moves in a straight line such that its acceleration a is given by a=2(4-t)^1/2, 0≤t≤4. If it starts at rest, find an expreesion fot the velocity v where a =dv/dt.
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Solution:The acceleration is, a=2%284-t%29%5E%281%2F2%29, where, 0≤t≤4
To find the velocity of the point, we integrate the acceleration:
int%282%284-t%29%5E%281%2F2%29%2C+dt%2C+0%2C+%0D%0A%0D%0A4%29= Substitute u=4-t then, du=-dt and dt=-du.
2%2A+int%28u%5E%281%2F2%29%2C+du%2C+0%2C+4%29=
%28-4%2F3%29u%5E%283%2F2%29, at (0, 4)
Substitute and have: 0-(-4/3)(4)^(2/3)=32/3 m/s.