You are standing at rest at a bus stop. A bus moving at a constant speed of 5.00 m>s passes you. When the rear of the bus is 12.0 m past you, you realize that it is your bus, so you start to run 2 toward it with a constant acceleration of 0.960 m>s.

A) How far would you have to run before you catch up with the rear of the bus?

B) How fast must you be running then? Find the final speed just as you reach the bus.

C) Would an average college student be physically able to accomplish this? Yes or No

A) You have to run 73.8 m before you reach the rear of the bus.

B) When you catch the bus, your velocity will be 11.9 m/s.

C) No, an average college student would not reach the bus.

Explanation:

Hi there!

The equations of velocity and position that we will use are the following:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t.

x0 = initial position.

v0 = initial velocity.

t = time.

a = acceleration.

v = velocity at time t.

A) First, let's find the time at which you catch the bus. At this time, the position of the bus and yours are the same:

When you catch the bus:

Bus position = your position

The equation of position of the bus with constant velocity is the following:

x = x0 + v · t

You have a constant acceleration, so your position will be given by the equation of position described above:

x = x0 + v0 · t + 1/2 · a · t²

If we place the origin of the frame of reference at the bus stop, your initial position is zero (and the initial position of the bus is 12.0 m). Since you start from rest, your initial velocity is also zero. Then:

Bus position = your position

x0 + v · t = 1/2 · a · t²

12.0 m + 5.00 m/s · t = 1/2 · 0.960 m/s² · t²

0 = 0.48 m/s² · t² - 5.00 m/s · t - 12.0 m

Solving the quadratic equation for t:

t = 12.4 s

You catch the bus in 12.4 s, now, we have to find the distance you run in that time:

x = x0 + v0 · t + 1/2 · a · t²

Since x0 and v0 = 0

x = 1/2 · a · t²

x = 1/2 · 0.960 m/s² · (12.4 s) ²

x = 73.8 m

You have to run 73.8 m before you reach the rear of the bus.

B) Now, let's use the equation of velocity to find your velocity at t = 12.4 s.

v = v0 + a · t

Since v0 = 0:

v = a · t

v = 0.960 m/s² · 12.4 s

v = 11.9 m/s

When you catch the bus, your velocity will be 11.9 m/s.

C) The record of Usain Bolt is 12.4 m/s. You would have to run almost as fast as Usain Bolt to catch the bus. So the answer is no, an average college student would not reach the bus.