Question

Which of the following is the correct relationship among the acceleration, velocity, and position?

1. ads = vdv
2. adv = sds
3. vda = sds
4. sda = vdv

Answer 1

option (1)

Step-by-step explanation:

Acceleration is defined as the rate of change of velocity with respect to time.

a = dv / dt

where, dv is the change in velocity and dt is the change in time.

So,
`a = (dv)/(dt)* (ds)/(ds)`

`a = (dv)/(ds)* (ds)/(dt)`

So, a ds = v dv

Thus, option (1) is correct.

Answer 2

Answer:1

Step-by-step explanation:

If

s=displacement

v=velocity of particle

a=acceleration of particle

acceleration can be written as rate of change of velocity

so
`a=\frac{\mathrm{d} v}{\mathrm{d} t}`

multiply and divide by
`ds`

`a=\frac{\mathrm{d} v}{\mathrm{d} t}* (ds)/(ds)`

`a=\frac{\mathrm{d} v}{\mathrm{d} s}* \frac{\mathrm{d} s}{\mathrm{d} t}`

`a=v\frac{\mathrm{d} v}{\mathrm{d} s}`

`ads=vdv`

option 1 is correct