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erastova [34]
3 years ago
6

Derive the formula v= u+ atplease derive in detail ​

Physics
2 answers:
lesantik [10]3 years ago
7 0

Answer:

pagal hai ye

Explanation:

mark me as brainliest ❤️

gogolik [260]3 years ago
4 0

Lets do

We know

The rate of change of velocity is acceleration .

\\ \sf\longmapsto a=\dfrac{dv}{dt}

\\ \sf\longmapsto dv=adt

Integrate both sides

\\ \sf\longmapsto \int dv=a\int dt

As acceleration is constant .Take it outside of integral .On velocity we can take limit u to v and time from 0 to t

\\ \sf\longmapsto {\displaystyle{\int}}^v_u dv=a{\displaystyle{\int}}^t_0 dt

Hence

\\ \sf\longmapsto v{\huge{|}}^v_u=at

\\ \sf\longmapsto v-u=at

\\ \sf\longmapsto v=u+at

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Based on observations, the speed of a jogger can be approximated by the relation v 5 7.5(1 2 0.04x) 0.3, where v and x are expre
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solution:

to find the speed of a jogger use the following relation:  

V

=

d

x

/d

t

=

7.5

×m

i

/

h

r

...........................(

1

)  

in Above equation in x and t. Separating the variables and integrating,

∫

d

x

/7.5

×=

∫

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C

or

−

4.7619  

=

t

+

C

Here C =constant of integration.   

x

=

0  at  t

=

0

, we get:  C

=

−

4.7619

now we have the relation to find the position and time for the jogger as:

−

4.7619  =

t

−

4.7619

.

.

.

.

.

.

.

.

.

(

2

)

Here

x  is measured in miles and  t  in hours.

(a) To find the distance the jogger has run in 1 hr, we set t=1 in equation (2),    

     to get:

      = −

4.7619  

      =  

1

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4.7619

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i

l

e

s

(b) To find the jogger's acceleration in   m

i

l

/

differentiate  

     equation (1) with respect to time.

     we have to eliminate x from the equation (1) using equation (2).  

     Eliminating x we get:

     v

=

7.5×

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d

v/

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t

       =

−

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/

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      t

=

0

      the joggers acceleration is :

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1

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