The final velocity of an object moving in one dimension is given by the formula [tex]$v=u+a t$[/tex], where [tex]$u$[/tex] is the initial velocity, [tex]$a$[/tex] is the acceleration, and [tex]$t$[/tex] is the time. Solve this equation for [tex]$t$[/tex].
To solve for [tex]$t$[/tex], first subtract [tex]$u$[/tex] from both sides of the equation.
Subtracting [tex]$u$[/tex] from both sides of the equation results in:
[tex]$v-u=a t$[/tex]
Solve this equation for [tex]$t$[/tex].
A. [tex]$t=(v-u)-a$[/tex]
B. [tex]$t=(v-u)+a$[/tex]
C. [tex]$t=a(v-u)$[/tex]
D. [tex]$t=(v-u) / a$[/tex]
Answer (2)
Subtract u from both sides of the equation: v ā u = a t .
Divide both sides by a : t = a v ā u ā .
The solution for t is: t = a v ā u ā ā .
Explanation
Understanding the Equation We are given the equation v = u + a t , where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Our goal is 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 ā u = u + a t ā u
v ā u = a t
Solving for t Next, to solve for t , we divide both sides of the equation by a , assuming a e q 0 :
a v ā u ā = a a t ā
a v ā u ā = t
Final Answer Therefore, the solution for t is:
t = a v ā u ā
Examples
In physics, this formula is fundamental for calculating the time it takes for an object to reach a certain velocity under constant acceleration. 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/sĀ², we can use this formula to find the time it takes to reach that final velocity. Plugging in the values, we get t = 3 25 ā 10 ā = 5 seconds. This concept is crucial in understanding motion and is applied in various fields like engineering, sports science, and aerospace.
To find t in the equation v = u + a t , subtract u from both sides to get v ā u = a t , and then divide by a . Thus, the formula for time is t = a v ā u ā .
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