I was so sure I had gotten this acceration problem right

[sweetdaisy186]

Hey guys

I was really confident that I had done this problem right. I have no idea where I went wrong. :(

A car accerlation from rest to a speed of 40 mi/hr in 12s. How far does the car travel during this time?

I remembered my teacher saying that speed is equal to the distance over time. So I thought that I could solve for this distance using that equation. I converted the 40 mi/hr into 0.01787 m/s and then multiplied by 15s to get a really small number. I think I messed up somewhere. Could I please have a hint? Thanks!

 

[mezarashi]

Firstly, I think you did some math wrong. 40 miles per hour is clearly faster than 0.01787 meters per second. That's not even 2 centimeters per second ! You've been on a car before and I think you know it moves _slightly_ faster than that ^^. Sanity checks are always useful in physics to check your own work.

I don't know if you have been introduced to the kinematics equations yet? You can't use your intuitive d = vt because there is acceleration involved and velocity is not constant! That equation only works when there is no acceleration. They are equations that look like this:

$$d = v_i t + \frac{1}{2}at^2$$
$$v_f^2 = v_i^2 + 2ad$$

which is derived using calculus. It describes the distance $$d$$ traveled by someone or something given an initial velocity $$v_i$$ and an acceleration $$a$$ over a period of time $$t$$. Just check up on your calculations and you should be good ^^.

 

[sweetdaisy186]

HI!

I have been introduced to the equations that you posted, but I didn't think I could use it because I didn't know what to put for velocity since it only gave acceration and time. Can I just assume that it is zero?

 

[mezarashi]

When you're solving a physics problems, don't just look for the numbers! You're trying to understand the situation as well as the equation you are using. It says the car is "starting from rest". What does that tell you about the initial velocity. It says the car attains a speed of 40 miles/hr in the end. In fact, they don't tell you the value for acceleration. There's also another equation to the series ^^:

$$v_{final} = v_{initial} + at$$

 

[sweetdaisy186]

The initial velocity has to be zero since it is starting from rest. So I should solve for the acceleration correct? After I use your equation I can use the first equation that you gave me to find the final answer. This is my theory...

 

[Hootenanny]

The initial velocity has to be zero since it is starting from rest. So I should solve for the acceleration correct? After I use your equation I can use the first equation that you gave me to find the final answer. This is my theory...

Sounds good to me, just be careful with your unit conversions.

 

[sweetdaisy186]

I get it now. Thanks everyone for your help!