Finding Time from Accel and Distance

[BlueBob88]

Not school related, but I guess it could be a homework problem.
I am redoing my racing script on my car game and need some help. I have been looking around in many places and can't seem to find how to do this problem.

Homework Statement

I need to find the time it takes to travel 0.05 miles at a given acceleration starting at a given speed. I also need to find out the final speed.

So if a car starts from a stop (0 mph) and can travel 0-60mph in 7 seconds. How long will it take to travel 0.05 miles and what will its final speed be.

Homework Equations

time = change/acceleration
d=st

The Attempt at a Solution

So far I have its average acceleration at 8.57 mph/s if I can find the time I will be able to find its final speed. If its 1 second it will be 8.75 mph, 2 seconds will be 35mph. (Not to sure on that) But I did (2 seconds^2) * 8.75

 

[Feldoh]

Is it going to be a constant acceleration? If it is you can use

$$(V_f)^2=(V_i)^2+2a(d_f)$$

Where $$V_f =$$ Final Velocity, $$V_i =$$ Initial Velocity, $$d_f =$$ the final displacement.

From there you can find the time it takes in a multitude of ways.

 

[m2003]

mph to get the distance.

I would approach this problem by first understanding the relationship between acceleration, distance, and time. The equation d=st can be rearranged to t=d/s, where t is time, d is distance, and s is speed. This means that to find the time it takes to travel 0.05 miles, we need to divide the distance by the speed.

Next, we need to consider the acceleration of the car. From the given information, we know that the car can go from 0-60mph in 7 seconds. This means that the average acceleration during that time period is 60mph/7s = 8.57 mph/s. However, this is the average acceleration and may not be the same as the acceleration at a specific moment in time.

To find the acceleration at a specific moment, we can use the formula a=(vf-vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time. In this case, we know that the initial velocity is 0 mph and the final velocity is 60 mph. We also know that the time is 7 seconds. Plugging these values into the equation, we get a= (60mph-0mph)/7s = 8.57 mph/s. This confirms our previous calculation.

Now, to find the time it takes to travel 0.05 miles, we can use the equation t=d/s. Plugging in the values, we get t=0.05 miles/60mph = 0.000833 hours. This is equivalent to 0.05 minutes or 3 seconds. This means that it will take the car 3 seconds to travel 0.05 miles.

To find the final speed, we can use the equation vf=vi+at, where vf is final velocity, vi is initial velocity, a is acceleration, and t is time. Plugging in the values, we get vf= 0mph + (8.57 mph/s)(3s) = 25.71 mph. This means that the car will reach a speed of 25.71 mph after traveling 0.05 miles.

In conclusion, as a scientist, I would approach this problem by first understanding the relationships between acceleration, distance, and time, and then using equations to calculate the desired values. I would also double check my calculations and consider any potential sources of