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​A particle moves with a deceleration √v Initial velocity is Vo. Find the time after which it will stop

​A particle moves with a deceleration √v
Initial velocity is Vo. Find the time after which it
will stop

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Grade:11

2 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
v = u -at 
u = vo = initial velocity 
Acceleration = √v
Time taken by particle to stop = t 
t = (v-v0)/a = -vo/√v
Good Luck 
MAHESH KUMAR
13 Points
4 years ago
a= -v½
\frac{dv}{v^{1/2}}= -dt
\int_{v\circ }^{0}\frac{dv}{v^{1/2}}=-\int_{0}^{t}dt
[\frac{v^{1/2}}{1/2}] v\circ \rightarrow 0 = -[t - 0]      the integration is from v\circ to zero 
-\frac{v\circ ^{1/2}}{1/2}=-t
t=2v\circ ^{1/2}  This is the answer.
All I have done is formed an equation as given in the question, variables being a and v.
Then, I wrote a in terms of dv/dt and did further calculations to get t when velocity becomes zero
 
 

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