Grade 12Mechanics

Is there something special when an object moves according to the law v=asqrt(s) ?

v -velocity
a-constant
s-displacement

actually, the acceleration for this type of motion comes out to be constant.
dv/dt=dv/dsds/dt
= [a/2sqrt(s)]a.sqrt(s)=a^2/2
can you intuitively explain why this happens ?

shubham tomar

15 Years agoGrade 12

2 Answers

vikas askiitian expert

15 Years ago

v=ds/dt=Ksqrt(s) (k=a^2/2)

ds/sqrt(s)=kdt

2sqrts=kt+c

s=(kt+c)^2 /2

it means graph between time and displacement is parabola......

Askiitians_Expert Yagyadutt

15 Years ago

Hiii shubham

v = a root(x)

dx/dt = a.root(x)

dx/a.root(x) = a.dt

Integrate it ...

2root(x) = a .t

or x = a^2.t^2/4

x = kt^2

This is a parabolic path with respect to time..

d^2x/dt^2 = 2k ( constant )

So this is just a projectile motion with object starting from rest...moved with constant acceleration 2k

Regards

Yagya

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Is there something special when an object moves according to the law v=a*sqrt(s) ? v -velocitya-constants-displacementactually, the acceleration for this type of motion comes out to be constant.dv/dt=dv/ds*ds/dt= [a/2*sqrt(s)]*a.sqrt(s)=a^2/2can you intuitively explain why this happens ?

shubham tomar

2 Answers

vikas askiitian expert

Askiitians_Expert Yagyadutt

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Is there something special when an object moves according to the law v=asqrt(s) ?

v -velocity
a-constant
s-displacement

actually, the acceleration for this type of motion comes out to be constant.
dv/dt=dv/dsds/dt
= [a/2sqrt(s)]a.sqrt(s)=a^2/2
can you intuitively explain why this happens ?

A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.

11
21
31
41