What Was the Initial Speed of the Bicycle Going Downhill?

[harujina]

Homework Statement

A student riding a bicycle begins to go downhill and accelerates at a rate of 1.8m/s2. If the acceleration lasts for 2.4s, and the final speed of the bicycle is 10.2m/s, at what speed was he initially travelling?

a = 1.8
t = 2.4
vf = 10.2

vi = ?

Homework Equations

a = vf - vi / t

The Attempt at a Solution

I first isolated vi to solve for the problem and got : vi = vf-a/t and then plugged in the variables but it didn't work.

 

[SteamKing]

a = (vf - vi) / t is the correct equation. Parentheses make a difference. Also, using correct algebra.

However, this equation is good only over short time intervals.

 

[collinsmark]

Homework Statement

A student riding a bicycle begins to go downhill and accelerates at a rate of 1.8m/s2. If the acceleration lasts for 2.4s, and the final speed of the bicycle is 10.2m/s, at what speed was he initially travelling?

a = 1.8
t = 2.4
vf = 10.2

vi = ?

Homework Equations

a = vf - vi / t

Be careful with your parenthesis, they make a difference.

the correct equation for uniform acceleration is

a = ( v_f - v_i )/t

The Attempt at a Solution

I first isolated vi to solve for the problem and got : vi = vf-a/t and then plugged in the variables but it didn't work.

There's an algebra mistake in there somewhere. It shouldn't contain the term a divided by t. It's something else.

[Edit: SteamKing beat me to the response.]

 

[harujina]

Ok, then is this correct?:

a = (vf - vi)/t
at = vf - vi
at + vi = vf
vi = vf - at

 

[SteamKing]

Looks Good

 

[harujina]

Ohh, I was so confused since I thought I had to divide t from both sides since it was a*t...
Anyways, thank you!