Ariana is accelerating her car at a rate of 4.6 m/s² for 10 seconds. What was her final velocity?
A. 0 m/s
B. 2.3 m/s
C. 4.6 m/s
D. 46 m/s
Answer (1)
We are given the acceleration and time, and we need to find the final velocity.
We use the formula: v f = v i + a \t
Substituting the given values: v f = 0 + ( 4.6 \t m / s 2 ) ( 10 \t s )
The final velocity is: 46 \t m / s
Explanation
Understanding the Problem We are given that Ariana is accelerating her car at a rate of 4.6 m/s² for 10 seconds. We need to find her final velocity. We assume the initial velocity is 0 m/s.
Stating the Formula We can use the formula for final velocity when there is constant acceleration: v f = v i + a \t , where: v f is the final velocity, v i is the initial velocity, a is the acceleration, and t is the time.
Identifying the Given Values We are given: v i = 0 \t m / s (since the car starts from rest), a = 4.6 \t m / s 2 , and t = 10 \t s .
Substituting the Values Now, we substitute the given values into the formula: v f = 0 + ( 4.6 \t m / s 2 ) ( 10 \t s ) .
Calculating the Final Velocity Calculating the final velocity: v f = 46 \t m / s .
Final Answer Therefore, Ariana's final velocity is 46 m/s.
Examples
Understanding motion with constant acceleration is crucial in many real-world scenarios. For instance, when designing a runway for airplanes, engineers need to calculate the minimum length required for a plane to reach its takeoff speed, considering its acceleration and initial velocity. Similarly, in vehicle safety, knowing the acceleration and braking capabilities helps determine the stopping distance and prevent accidents. This problem illustrates a fundamental concept used in these applications.
