An object is moving at a speed of 3 + 2 𝑓𝑡/𝑠. How long would it take the
object to travel 20 𝑓𝑡? [looking for actual solution and not decimal approximation]
To determine how long it would take for the object to travel 20 ft, we need to set up an equation using the given information.
The speed of the object is given as 3 + 2𝑓𝑡/𝑠, where 𝑓𝑡 represents time in seconds. The unit of speed is ft/s.
Let's set up the equation:
Distance = Speed × Time
We want to find the time it takes for the object to travel 20 ft. So, we can write:
20 𝑓𝑡 = (3 + 2𝑓𝑡/𝑠) × 𝑓𝑡
Now, let's solve for 𝑓𝑡.
First, distribute the 𝑓𝑡 on the right-hand side:
20 𝑓𝑡 = 3𝑓𝑡 + (2𝑓𝑡/𝑠) × 𝑓𝑡
Combine the like terms:
20 𝑓𝑡 = 3𝑓𝑡 + 2𝑓𝑡²/𝑠
Rearrange the equation to isolate the quadratic term:
2𝑓𝑡²/𝑠 = 20 𝑓𝑡 - 3𝑓𝑡
2𝑓𝑡²/𝑠 = 17 𝑓𝑡
Now, divide both sides by 2𝑓𝑡/𝑠:
2𝑓𝑡/𝑠 = 17
Finally, solve for 𝑓𝑡 by multiplying both sides by 𝑠/2:
𝑓𝑡 = 17𝑠/2
So, the time it would take for the object to travel 20 ft is given by the equation 𝑓𝑡 = 17𝑠/2.