Deriving d = 1/2 a t2: Intro Physics Proof

[cosmic-barley]

Homework Statement

Show a derivation of d = 1/2 a t2

Homework Equations

hint: v=a*t

The Attempt at a Solution

I'm not sure how to attempt this. to be perfectly frank I am not well versed in physics/mathematics. If anyone could be of assistance, i would be most grateful.

 

[Benzoate]

take the derivative of d with respect to t and that will give you the velocity.

 

[m2003]

No problem! I can help you with this derivation.

Firstly, let's define the variables:
d = displacement
a = acceleration
t = time

We know that velocity (v) is equal to the change in displacement over the change in time, or v = d/t. We also know that acceleration (a) is equal to the change in velocity over the change in time, or a = v/t. So we can rewrite these equations as:

v = d/t
a = v/t

We can rearrange the first equation to solve for d:

d = v*t

And we can substitute this into the second equation, since we know that v = a*t:

a = (a*t)/t

Simplifying this, we get:

a = a

This shows that the acceleration is equal to itself, which is true. Now, we can rearrange the first equation again to solve for v:

v = d/t

And we can substitute this into the second equation, since we know that a = v/t:

a = (d/t)/t

Simplifying this, we get:

a = d/t^2

Now, we can rearrange this equation to solve for d:

d = a*t^2

And finally, we can divide both sides by 2 to get the final equation:

d = 1/2 a t^2

And there you have it! We have derived the equation d = 1/2 a t^2 using basic principles of physics and algebra. I hope this helps you understand the derivation better. Keep practicing and you'll become more comfortable with physics and math in no time!