Question : An object falling through a fluid observed to have acceleration given by a=g-bv where g is the gravitational acceleration and b is a constant. After a long time it is observed to fall with constant velocity. what would be the value of this constant velocity?
Doubt by Divya
Solution :
We know,
a=g-bv
Hence, the value of constant velocity would be g/b.
Alternate Method :
Alternate Method :
a=g-bv — (1)
After long time velocity becomes constant so
a=dv/dt
a=d(const)/dt
a=0
Putting in equation (1)
0=g-bv
bv=g
v=g/b
After long time velocity becomes constant so
a=dv/dt
a=d(const)/dt
a=0
Putting in equation (1)
0=g-bv
bv=g
v=g/b
Hence, the value of constant velocity would be g/b.