Finding Initial Velocity with Given Acceleration Ratio

[jacksonpeeble]

Homework Statement

A car is traveling along a straight road at a velocity of +38.0 m/s when its engine cuts out. For the next ten seconds, the car slows down, and its average acceleration is a1. For the next five seconds, the car slows down further, and its average acceleration is a2. The velocity of the car at the end of the fifteen-second period is +22.6 m/s. The ratio of the average acceleration values is a1/a2 = 1.53. Find the velocity of the car at the end of the initial ten-second interval.

Homework Equations

Well, perhaps v = v0 + at has something to do with this.

The Attempt at a Solution

Unfortunately, as simple as it sounds, I'm somewhat stumped. What I don't understand is where the ratio comes into play, and how to combine all of this information in an equation. If somebody could point me in the right direction, I'll try to solve this problem on the forum before asking for a solution.

Thank you very much for any assistance!

 

[rock.freak667]

well if a =(v-u)/t

Now a₁= (v₁-38)/10

for a₂, the initial velocity is v₁ and the final is 22.6.


You can now easily find what a₁/a₂ is using these equations and set that equal to 1.53 and get v₁

 

[jacksonpeeble]

well if a =(v-u)/t

Now a₁= (v₁-38)/10

for a₂, the initial velocity is v₁ and the final is 22.6.


You can now easily find what a₁/a₂ is using these equations and set that equal to 1.53 and get v₁

Oh... that makes sense. ;-)

So, in summary:

((v₁-38)/10)/((22.6-v₁)/5)=1.53, v₁=26.393

Thank you!