Solving for time when given distance and acceleration,

[jkmjkm]

Problem: How long will it take a car to cover a distance of 125 m if it accelerates at 4.0m/s^2 for 9.0 sec?
I'm in an intro to physics course. Our teacher has taught us nothing about quadratics yet. He has, in fact, taught us very little. Friends have tried to teach me how to solve this question using the " D = .5*a*T^2" equation, but I just can't grasp it. Since using the quadratic formula hasn't even been mentioned in class, I feel like that's the not the way he wants us to solve it. Is there another way to solve this question?
Solution attempt: 1/2at^2 + v0t - s = 0 is all my friends have given me. I am completely lost.

 

[Redbelly98]

Problem: How long will it take a car to cover a distance of 125 m if it accelerates at 4.0m/s^2 for 9.0 sec?



I'm in an intro to physics course. Our teacher has taught us nothing about quadratics yet. He has, in fact, taught us very little. Friends have tried to teach me how to solve this question using the " D = .5*a*T^2" equation, but I just can't grasp it. Since using the quadratic formula hasn't even been mentioned in class, I feel like that's the not the way he wants us to solve it. Is there another way to solve this question?



Solution attempt: 1/2at^2 + v0t - s = 0 is all my friends have given me. I am completely lost.

Welcome to Physics Forums.

Before providing some help, I just need to mention a few things. These are meant to both help you in your physics class and any future science classes, as well as some guidelines for getting help at our forum, so I hope you take them in the constructive spirit intended.

1. By the time you are taking physics, it is pretty much expected that you know what you have been taught in your algebra and geometry classes. This includes knowing about the quadratic formula.

2. Please don't post in all-bold font for your entire post. As one of the forum moderators, I have taken the liberty of editing it to remove most of the bolding.

3. Please leave the homework template intact in future posts (the thing that says "1. The problem statement", etc. etc.)

That being said: yes, the equation "1/2at^2 + v0t - s = 0 " works for solving this problem. But it is usually given in the form

s = v0t + 1/2at^2​

At any rate, you need to think about what the value of v0 is in this problem. No, they don't tell you explicitly in the problem statement, but common sense should help you out here.

Hope that helps, and again welcome to PF.

 

[Redbelly98]

I just noticed you posted another equation, "D = .5*a*T^2". You don't actually need the quadratic equation here, you can solve that equation for "T" without the quadratic equation. Post back if still need help with that.

 

[jkmjkm]

Is there a way to delete this thread? Because I've already solved it using t = the square root of d / a...

I'm in a pre-health program, so we're being taught the very basics and then we're getting into the more "involved" stuff later in the semester. We haven't learned about quadratics in math yet, so we wouldn't be using quadratic formulas in physics.

 

[Nickie]

I understand your frustration and confusion with this problem. It is important to note that there are multiple ways to solve this question and the method your friends have shown you is one of them. However, since you have not been taught about quadratics in your class, there may be another approach that your teacher is expecting you to use.

One possible way to solve this problem is by using the formula t = √(2d/a), where t is the time, d is the distance, and a is the acceleration. Plugging in the given values, we get t = √(2*125/4.0) = √(62.5) = 7.91 seconds. This formula can be derived from the equation you mentioned, 1/2at^2 + v0t - s = 0, by solving for t using the quadratic formula.

Another approach could be to use the equation v = u + at, where v is the final velocity, u is the initial velocity (which is assumed to be 0 in this case), a is the acceleration, and t is the time. Rearranging this equation to solve for t, we get t = v/a. Since we know the final velocity (v) is 4.0m/s and the acceleration (a) is 4.0m/s^2, we can plug in these values to get t = 4.0/4.0 = 1 second. This is the time it takes for the car to achieve its final velocity, and we can then add this time to the given 9 seconds of acceleration to get a total time of 10 seconds.

It is important to note that both of these methods assume constant acceleration, meaning the car is accelerating at a constant rate of 4.0m/s^2 for the entire 9 seconds. If this is not the case, then the problem becomes more complex and may require a different approach.

In conclusion, there are multiple ways to solve this problem and it is important to understand the underlying principles and equations involved. If you are still unsure, I would recommend speaking with your teacher for clarification on the expected method of solving this problem.