For an object starting from rest and accelerating with constant acceleration, distance traveled is proportional to the square of the time. if an object travels 2.0 furlongs in the first 2.0 s, how far will it travel in the first 4.0 s?

The problem states that the distance travelled (d) is directly proportional to the square of time (t^2), therefore we can write this in the form of:

d = k t^2

where k is the constant of proportionality in furlongs / s^2

Using the 1st condition where d = 2 furlongs, t = 2 s, we calculate for the value of k:

2 = k (2) ^2

k = 2 / 4

k = 0.5 furlongs / s^2

The equation becomes:

d = 0.5 t^2

Now solving for d when t = 4:

d = 0.5 (4) ^2

d = 0.5 * 16

d = 8 furlongs

It traveled 8 furlongs for the first 4.0 seconds.