The equation [tex]f=v+at[/tex] represents the final velocity of an object, [tex]f[/tex], with an initial velocity, [tex]v[/tex], and an acceleration rate, [tex]a[/tex], over time, [tex]t[/tex]. Which is an equivalent equation solved for [tex]t[/tex]?
A. [tex]t=\frac{f-v}{a}[/tex]
B. [tex]t=\frac{f-a}{v}[/tex]
C. [tex]t=a(f-v)[/tex]
D. [tex]t=v(f-a)[/tex]
Answer (1)
Start with the equation f = v + a t .
Subtract v from both sides: f − v = a t .
Divide both sides by a : t = a f − v .
The equivalent equation solved for t is t = a f − v .
Explanation
Understanding the Problem We are given the equation f = v + a t and asked to solve for t . This involves isolating t on one side of the equation using algebraic manipulations.
Isolating the term with t First, subtract v from both sides of the equation to isolate the term with t : f − v = v + a t − v f − v = a t
Solving for t Next, divide both sides of the equation by a to solve for t :
a f − v = a a t a f − v = t
Final Answer Therefore, the equation solved for t is: t = a f − v
Examples
In physics, this equation is fundamental for calculating motion. For example, if you know the final speed of a car, its initial speed, and how quickly it accelerated, you can use this equation to find out how long it took to reach that final speed. This is useful in many real-world scenarios, such as designing safer cars or planning efficient transportation systems.
