Question

You are trying to get to class on time using the UCF Shuttle. In 45.2 m, you will reach a barrier, and you must catch the shuttle before that point. The shuttle has a constant acceleration of

4.6m/s² . What is the minimum velocity you have to run at to catch the bus before it reaches the barrier?
A. 6.8m/s
B. 8.6m/s
C. 12.3m/s
D. 16.9m/s

Answer 1

To catch the shuttle before it reaches the barrier, you need to reach the same distance in a shorter time. Using the equation v = u + at, and plugging in the given values, the minimum velocity is approximately 45.07 m/s.

Step-by-step explanation:

To catch the shuttle before it reaches the barrier, you need to reach the same distance in a shorter time. The minimum velocity can be calculated using the equation:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Since the shuttle has a constant acceleration of 4.6 m/s² and the distance is 45.2 m, let's assume the initial velocity is 0 m/s. Plugging in the values, we get:

v = 0 + 4.6t

45.2 = 0 + 4.6t

t = 45.2 / 4.6

t ≈ 9.83 s

Now we can plug this value of t back into the equation to find the minimum velocity:

v = 0 + 4.6(9.83)

v ≈ 45.07 m/s

Therefore, the minimum velocity you have to run at to catch the bus before it reaches the barrier is approximately 45.07 m/s.