How Do You Solve for Acceleration and Velocity in Basic Physics Equations?

[mrthomas]

Homework Statement

Question #1:

Δd=v¹Δt+½a(t)²

Solve for: a

Question #2:

E= ½ m * v²
Solve for: v

Homework Equations

Δd=v¹Δt+½a(t)²
v = Δd / Δt
a = v² - v¹ / Δt
v² = v¹ + a * Δt
Δd = (v² - v¹) * Δt
Δd = v¹ * Δt + ½ a ( Δt )²
E= ½ m * v²

The Attempt at a Solution

I'm not sure how to resolve this one.

 

[learningphysics]

Just solve for a in the first equation... just like normal algebra... rearrange the equation etc...

 

[Astronuc]

Δd=v¹Δt+½a(t)²

One needs to be consistent.

This equation assumes constant acceleration, and t would be the elapsed time from application of the acceleration. v¹ would normally the initial velocity (or speed) at the reference time, and d would be the distance at time t.

See this - http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

and

http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html

As learningphysics indicated, one can solve algebraically for the variables or coefficients in terms of variables and other coefficients.