Question

The distance traveled by an object can be modeled by the equation d = ut + 0.5^2 where d = distance, u = initial velocity, t= time, and a = acceleration. solve this formula for a. show all steps in your work.

Answer 1

Your equation is not quite right: It should be d = ut + 0.5*a*t^2.

In this case, solving for a is easy.

Fist you want to isolate the variable on one side of the equation. To accomplish this we subtract ut from both sides of the equation.

d - ut = ut - ut + 0.5*a*t^2

d - ut = 0.5*a*t^2

Now multiply both sides by 2, in order to get rid of the '0.5' in front of the a^2.

2(d-ut) = 2(0.5*a*t^2)

2(d-ut) = a*t^2

Divide both sides by t^2:

2(d-ut)/t^2 = a

(2d/t^2) - (ut/t^2) = a

a = (2d/t^2) - (u/t)

\[a = \frac{ 2d }{ t^{2} } - \frac{ u }{ t }\]

\[a = \left( \frac{ 1 }{ t } \right)\left( \frac{ 2d }{ t } - u\right)\]