Solve a Literal Equation
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].
Answer (2)
To solve for time t in the equation v = u + a t , isolate t by first subtracting u from both sides and then dividing by a . The final formula is t = a v − u . This is useful in various kinematic calculations where the relationship between velocity, acceleration, and time is needed.
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Subtract u from both sides: v − u = a t .
Divide both sides by a : t = a v − u .
The solution for t is t = a v − u .
Explanation
Understanding the Problem We are given the equation 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 = a t .
Solving for t Next, we divide both sides of the equation by a to isolate t . This gives us t = a v − u .
Final Answer Therefore, the solution for t is t = a v − u .
Examples
In physics, this formula is used to calculate the time it takes for an object to reach a certain final velocity given its initial velocity and 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/s², 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 − 10 = 5 seconds. This shows how rearranging formulas allows us to solve for different variables in real-world scenarios.
