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

Answer:1

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 $ds$

$a=\frac{\mathrm{d} v}{\mathrm{d} t}\times \frac{ds}{ds}$

$a=\frac{\mathrm{d} v}{\mathrm{d} s}\times \frac{\mathrm{d} s}{\mathrm{d} t}$

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

$ads=vdv$

option 1 is correct

Answer 2

Answer:

option (1)

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, $a = \frac{dv}{dt}\times \frac{ds}{ds}$

$a = \frac{dv}{ds}\times \frac{ds}{dt}$

So, a ds = v dv

Thus, option (1) is correct.