Question

A car is traveling along a straight road at a velocity of +34.4 m/s when its engine cuts out. For the next 2.98 seconds, the car slows down, and its average acceleration is . For the next 6.04 seconds, the car slows down further, and its average acceleration is . The velocity of the car at the end of the 9.02-second period is +27.1 m/s. The ratio of the average acceleration values is = 1.33. Find the velocity of the car at the end of the initial 2.98-second interval.

Answer 1

Your question is missing some of the values

Answer 2

I think it's actually possible, and the missing accelerations are just blank because they are not given. A blank line ("_______") would be a good fit.

I hope this helps! I realized I maybe could have made this "solution" a little quicker, but I'm too tired to go through it again right now. I didn't give away answers or math, but if you read and understand this "solution," you should be able to calculate an answer. I might be on tomorrow, so feel free to ask for clarity, if necessary!

You don't know what the accelerations are.

You do have the ratio between the two, though. My biggest complaint is that it doesn't say if the ratio is the first acceleration to the second, like\[\large 1.33=\frac{\text{first accel.}}{\text{second accel.}}\]I'll assume it's that, though.
Rearranged, we see that\[1.33\times\text{second accel.} = \text{first accel.}\]

Now, remember; the first acceleration is for 2.98 seconds, and the second acceleration is for 6.04 seconds.

I see two ways to approach this. One is more physicsy, the other one is more number. I'll go with the physicsy one.

In each time period, the acceleration reduces the speed of the car.
If you knew the acceleration, you would be able to use\[\large a=\frac{\Delta v}{\Delta t}\\\Downarrow \\\Delta v=(a)(\Delta t)\]and find how much the car slows. We can still do this.

It's an old math trick. You're given a proportion, like\[1.33\times\text{second accel.} = \text{first accel.}\]and you substitute it in, like this:\[\Delta v_{first}=(a_{first})(\Delta t_{first})\\=(1.33 \times a_{second})(\Delta t_{first})\]

But you don't know the second acceleration. I mean you could try to solve for it, but what do you know? Well, I realized we can add the two changes in velocity, to get our total change in velocity. The addition of the two \[\Delta v=(a)(\Delta t)\] we have will get use the total change in velocity, which we can find out very quickly. We can then solve for the second acceleration.

Then you can calculate the first acceleration.

Since you now know the first acceleration, and how long it was in effect, you can find how much the velocity change in that time.

Once you know how much the velocity changed in the first time interval, you can use it to find the velocity after that first time interval. You can do it!

Again, ask if you have questions! Good luck!