Equations of Motion (Deriving equations)

[arjun90]

Hi, I am just wondering how you would approach this problem:
Using the definitions below, derive an equation for velocity as a function of acceleration and time (v=f(a,t)). Assume initial velocity is Vo. The answer to this problem is v=v0+a(t2-t1). My question is how would you arrive to this answer step-by-step. Below are the definitions:

x=current position in the x dimension
deltax= change in position
t=time now, t0 is the starting time.
deltat= a time interval, t2-t1.
v=deltax/deltat (use as a scaler for now).
deltav= a change in velocity.
a=deltav/deltat (Use as a scaler for now).

Subscripts: 0 is an initial value, other numbers are subsequent values in time order as needed.

v (average)= (v1+v2)/2, a simple average.

Any help will be appreciated. Thank you.

 

[sokratesla]

# I would first look at the definitaion of a
$$a(t) = \frac{dv(t)}{dt}$$
# Integrate both sides
$$\int^{t}_{t_0} a(t) dt = v(t) - v(0)$$
# This is the relation between v and a. but it is not in the form of you want, i.e. $$v=f(a,t)$$. It is an integral equation.
# So, there should be an assumption about a, which changes integral the relation between a and v to a function. I think if you think, you can find it by yourself.