Equations of motion with constant acceleration

Question 1

First equation of motion with constant acceleration

Answer 1

v = v_0 + a*t

Question 2

Second equation of motion with constant acceleration

Answer 2

x - x_0 = (v + v_0)*t/2

Question 3

Third equation of motion with constant acceleration

Answer 3

x = x_0 + v_0t + (at^2)/2

Question 4

Fourth equation of motion with constant acceleration

Answer 4

v^2 = v_0^2 + 2a(x - x_0)

Question 5

How to derive first equation

Answer 5

Since acceleration is constant, average acceleration = instantaneous acceleration. Rearrange average acceleration formula.

Question 6

How to derive second equation

Answer 6

Equate two different formulae for average velocity.

Question 7

How to derive third equation

Answer 7

Substitute first equation into second equation.

Question 8

How to derive fourth equation

Answer 8

Rearrange first equation in terms of t, substitute into second equation and rearrange.

Question 9

What does the first equation say?

Answer 9

Velocity is initial velocity plus constant acceleration times time

Question 10

What does the second equation say?

Answer 10

Position is initial position plus average velocity times time

Question 11

What does the third equation say?

Answer 11

Position is initial position plus initial velocity times time plus half of constant accelerations times time squared

Question 12

What does the fourth equation say?

Answer 12

Velocity squared is initial velocity squared plus two times constant acceleration times displacement between final and initial position