Distance covered under Constant Acceleration

[kananesgi]

I am not too good at math normally, so please accept my appologies if this is not the right forum. I really have no idea where this should be at.

My brother and I came up with a little math riddle and now we're not sure how to solve it. The riddle is this:

Two cars are on a road, travelling in the same direction. One car accelerates at a constant rate of 0-60mph in 15 seconds. The second car is moving at a constant speed of 60mph. If the first car is setting at a standstill, and begins to accelerate at the same moment that the second passes it, how much time and distance will the first car travel before it overtakes the second?

Now, the answer we are comming up with is 3/4 mile and about 45 seconds, but that is really more of a guess than anything else. Problem is I'm not sure how far the accelerating car would travel in a given time frame. I know from research that distance traveled under constant acceleration is directly correlated with the square of the time travelled. Meaning that at a constant rate of acceleration, the object travelling for 30 seconds will travel about 4 times further than it did in 15 seconds. Problem I'm having is I don't know how far the car would travel in any given amount of time at an acceleration rate of 240mph/minute (60mph/15 sec).

 

[Deleted member 4993]

I am not too good at math normally, so please accept my appologies if this is not the right forum. I really have no idea where this should be at.

My brother and I came up with a little math riddle and now we're not sure how to solve it. The riddle is this:

Two cars are on a road, travelling in the same direction. One car accelerates at a constant rate of 0-60mph in 15 seconds. {after 15 seconds - does it still keep on accelerating?}The second car is moving at a constant speed of 60mph. If the first car is setting at a standstill, and begins to accelerate at the same moment that the second passes it, how much time and distance will the first car travel before it overtakes the second?

Now, the answer we are comming up with is 3/4 mile and about 45 seconds, but that is really more of a guess than anything else. Problem is I'm not sure how far the accelerating car would travel in a given time frame. I know from research that distance traveled under constant acceleration is directly correlated with the square of the time travelled. Meaning that at a constant rate of acceleration, the object travelling for 30 seconds will travel about 4 times further than it did in 15 seconds. Problem I'm having is I don't know how far the car would travel in any given amount of time at an acceleration rate of 240mph/minute (60mph/15 sec).

This is a very good problem for solving graphically:
But algebraically
first convert

60 mph = 88 fps

acceleration = 88/15 fps^2

Then use equation

1/2 * 88/15 * t^2 = 88 * t

now solve for 't'

The distance ofcourse would be easy to calculate from the first car (constant speed).