Consult interactive solution 2.22 before beginning this problem. a car is traveling along a straight road at a velocity of +30.0 m/s when its engine cuts out. for the next 2.46 seconds, the car slows down, and its average acceleration is . for the next 6.79 seconds, the car slows down further, and its average acceleration is . the velocity of the car at the end of the 9.25-second period is +15.2 m/s. the ratio of the average acceleration values is = 1.66. find the velocity of the car at the end of the initial 2.46-second interval.

Let be the average acceleration over the first 2.46 seconds, and the average acceleration over the next 6.79 seconds.

At the start, the car has velocity 30.0 m/s, and at the end of the total 9.25 second interval it has velocity 15.2 m/s. Let be the velocity of the car after the first 2.46 seconds.

By definition of average acceleration, we have

and we're also told that

(or possibly the other way around; I'll consider that case later). We can solve for in the ratio equation and substitute it into the first average acceleration equation, and in turn we end up with an equation independent of the accelerations:

Now we can solve for . We find that

In the case that the ratio of accelerations is actually

we would instead have

in which case we would get a velocity of

b. a lightning bug, plug of grass, and a worm