Select the correct answer.
Given the following formula, solve for [tex]$t$[/tex].
[tex]$v=U+a t$[/tex]
A. [tex]$t=a(v-U)$[/tex]
B. [tex]$t=\frac{v+U}{a}$[/tex]
C. [tex]$t=\frac{v-U}{a}$[/tex]
D. [tex]$t=a(v+U)$[/tex]
Answer (1)
Subtract U from both sides: v − U = a t .
Divide both sides by a : t = a v − U .
The correct answer is t = a v − U .
Explanation
Understanding the Problem We are given the formula v = U + a t and asked to solve for t . This means we want to isolate t on one side of the equation.
Isolating the term with t First, we subtract U from both sides of the equation to get: v − U = U + a t − U v − U = a t
Solving for t Next, we divide both sides of the equation by a to isolate t :
a v − U = a a t a v − U = t
Finding the correct answer Therefore, t = a v − U . Comparing this to the given options, we see that it matches option C.
Examples
In physics, this formula relates final velocity ( v ) to initial velocity ( U ), acceleration ( a ), and time ( t ). If you know the final velocity, initial velocity, and acceleration of an object, you can use this formula to calculate how long it took to reach that final velocity. For example, if a car accelerates from an initial velocity of 10 m/s to a final velocity of 25 m/s with an acceleration of 3 m/s², we can calculate the time it took to accelerate using the formula: t = a v − U = 3 25 − 10 = 5 seconds.
