Question

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?

Short answer

object travel 8 furlongs in the first 4.0 s

Step-by-step solution

Step 1.Given information

Here the question is that if an object starting from rest and accelerating with constant

acceleration and the distance traveled by the object is directly proportional to the square of the time. then when if an object travels 2.0 furlongs in the first 2.0 s, then how much object will travel in the first 4.0 s.

Step 2 

distance travel by the object is directly proportional to the square of the time

$$\begin{gathered} s=\frac{1}{2}a{t}^2......\left(1\right) \\ where, \\ aisacceleration \\ sisdis\tan ceand \\ ts\tan dfortime \end{gathered}$$

Step 3 

consider the first condition where the value of distance is 2 furlongs and then time is taken to travel this distance is 2 s.

substitute all this value in equation (1) to find the value of a

$$\begin{gathered} s=\frac{1}{2}a\times t^2 \\ 2furlongs=\frac{1}{2}a\times {\left(2s\right)}^2 \\ a=\frac{4furlongs}{4s^2} \\ a=1furlongs/s^2.......\left(2\right) \end{gathered}$$

Step 4 

consider the second condition where the value of the distance unknown and given the time to travel the unknown distance is 4 s and the value of the acceleration is 1 furlongs

substitute all this value in equation (1) to find the value of distance

$$\begin{gathered} s=\frac{1}{2}a\times t^2 \\ s=\frac{1}{2}\times 1furlongs/s^2\times {\left(4s\right)}^2 \\ s=0.5furlongs/s^2\times 16s^2 \\ s=8furlongs \end{gathered}$$

Therefor, the object travel 8 furlongs in the first 4.0 s