A body starting from rest moves along a straight line with constant acceleration. Draw a v-s graph.?

Question

The graph will be curved(explain why?) and also give the solution to it.

Answer 1

Its simple:

a=dv/dt

so acceleration is proportional to the change in velocity over the change in time.

If you have constant acceleration or a goes up at a constant rate you have the equation:

k*a=k*dv/dt

This gives you the reason why the graph is curved.  Say time goes up by 1 each plot, and k = 2.  If you assume a=1 then

2*1 = 2

In this case, dv = 1 and dt = 1.   Now a=2 and t=2 and dt=1 because the change in time is 1.

2*2 = 4   :   4=k*dv/1   : 4=k*dv   2=dv

Okay, now you have two plots:

(v,s)=(1,1)(3,2)

Once more you see that

2*3 = 6 : 6=k*dv/1  : 3=dv

so now you have a change in velocity of 3, give you v=6

(v,s) = (1,1)(3,2)(6,3)

That plot will give you a curve.

Email me if you need anymore help with physics homework >.<

Answer 2

s = (1/2) a t^2

v = ds/dt = a t

v^2 = a^2 t^2 = 2a (1/2) a t^2

So:

v2 = 2as

v = 2a sqrt s

Graph of a square root function is a branch of a parabola with horizontal axis. (0, 0), (1, 2a), (4, 4a), (9, 6a)...are some points on the graph

Answer 3

Hey Gy-

No need for calculus here.

Take your two casic equations of motion for constant accel:

dist= avg. rate * time   s=(vf+vo)/2 *t

and vel=accel * time + init. vel  vf=at+vo

But you want the last equation (obtained by substitution)...

vf^2 = vo^2 + 2as

For ease of understanding, call init v (vo) zero.

This is a parabola.  Done.  No muss, no fuss, no calculus.

======================================...

A side note:

If you plug vf from eq. 2 into eq. 1, you get...

s=1/2 a t^2 + vo t

The curve of accel vs time is a parabola.

-Fred