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```        the acceleration of a certain marble is given by,
a=-3(velocity squared)
if the marble enters the fluid with a speed of 1.5m/s , how long will it take before marble's speed is reduced to half of its initial value?```
7 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear student,
a=-3v2
dv/dt=-3v2
dv/v2=-3dt
-1/v=-3t
So u get a relation between velocity and time..

All the best.
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Sagar Singh
B.Tech, IIT Delhi

```
7 years ago
510 Points
```										a = dv/dt
a = -3v2            (given)
dv/dt = -3v2
dv/v2 = -3dt
-1/v = -3t + c        .............1
at t=0 , v = 1.5
c = -2/3
now eq 1 becomes
-1/v = -3t + -2/3           ................2
finally velocity becomes half of original= v = 1.5/2
after putting this in eq 2 we get
t = 2/9 sec
t =
```
7 years ago
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