Question

velocity of a body is given by v=√200-8x meter per second were x is distance . find distance and Acceleration find using formula v²-u²=2as​

Answer 1

Answer:

We will use both of the equations of motion to reach the third equation of motion. This will require a bit of algebra.

S=ut+  

2

1

​  

at  

2

andv=u+at, include the time variant t

There will be some situations when we do not have any information about time and so it would be a good idea to derive an equation that does not have a t term.

To do this, we rearrange our first equation to get  

t=  

a

v−u

​  

 

and use this to replace t wherever it appears in the second equation. So

S=ut+  

2

1

​  

at  

2

 becomes,

S=u(  

a

v−u

​  

)+  

2

1

​  

a(  

a

v−u

​  

)  

2

 

⇒2aS=2u(v−u)+(v−u)  

2

 

⇒2aS=2uv−2u  

2

−v  

2

−2uv−u  

2

 

⇒2aS=v  

2

−u  

2

 

⇒v  

2

=u  

2

+2aS

Answer 2

We will use both of the equations of motion to reach the third equation of motion. This will require a bit of algebra.
S=ut+
2
1
​
at
2
andv=u+at, include the time variant t

There will be some situations when we do not have any information about time and so it would be a good idea to derive an equation that does not have a t term.
To do this, we rearrange our first equation to get
t=
a
v−u
​


and use this to replace t wherever it appears in the second equation. So
S=ut+
2
1
​
at
2
becomes,
S=u(
a
v−u
​
)+
2
1
​
a(
a
v−u
​
)
2

⇒2aS=2u(v−u)+(v−u)
2

⇒2aS=2uv−2u
2
−v
2
−2uv−u
2

⇒2aS=v
2
−u
2

⇒v
2
=u
2
+