Question

For an object starting from rest and accelerating with constantacceleration, distance traveled is proportional to the square of thetime. If an object travels 2.0 furlongs in the first 2.0 s, how far willit travel in the first 4.0 s?

Answer 1

Since the object is accelerating with constant acceleration we can use the following formula for the position of the object:

$x=x_0+v_0t+\frac{1}{2}at^2$

where x0 is the initial position, v0 is the initial velocity, a is the acceleration and t is the time. In this case, the initial position and velocity are zero. Plugging the values given we have:

$\begin{gathered} 2=\frac{1}{2}a(2)^2 \\ 2=2a \\ a=1 \end{gathered}$

Hence, the acceleration of the object is 1 furlong per second per second.

Once we know the acceleration we can use the same formula to determine how far the object will travel in four seconds.

$\begin{gathered} x=\frac{1}{2}(1)(4)^2 \\ x=\frac{16}{2} \\ x=8 \end{gathered}$

Therefore, the object will travel 8 furlongs in four seconds.