Car Velocity After Engine Cuts Out | Physics Problem

[Cursed]

Homework Statement

A car is traveling along a straight road at a velocity of +31.0 m/s when its engine cuts out. For the next ten seconds, the car slows down, and its average acceleration is a_1[/size]. For the next five seconds, the car slows down further, and its average acceleration is a_2[/size]. The velocity at the end of the fifteen-second period is +24.5 m/s. The ratio of the average acceleration values is a_1[/size]/a_2[/size] = 1.67. Find the velocity of the car at the end of the initial ten-second interval.

Homework Equations

V_F = V₀ + at

V_F = Final velocity
V₀ = Initial velocity
a = acceleration
t = time

The Attempt at a Solution

The answer is +26 m/s, but I don't know how to get it...

24.5 = 31.0 + a₂(15)

a₂ = -13/30 = -4.333...
a₁ = -3.8534

V_F = 31.0 + (-3.8534)(10)
V_F = -7.534

 

[Oerg]

Ok, do you know that you can find the average acceleration just by doing simple operations with the inidial velocity and the final velocity?And with that you can find the values of a1 and a2 through use of simultaneous equations. You should be able to solve from here.