Answer:
A) You would have to run 72.6 m.
B) You would have to run at a final speed of 11.8 m/s or 42.5 km/h.
C) No.
Explanation:
Hi there!
The equations for an object moving in a straight line with constant acceleration are as follows:
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
If the movement is with constant velocity, the same equations apply only that a = 0.
A) You will catch the bus when your position is the same as the position of the bus.
The equation of your position will be:
x = x0 + v0 * t + 1/2 a * t²
Since the center of the reference system is located at the point where you start running, x0 = 0. The initial velocity is 0 because you start from rest. Then:
x = 1/2 a * t²
The position of the bus will be:
x = x0 + v * t
Since you start running when the bus is 11.0 m past you, the initial position of the bus is 11.0 m.
If you catch the bus, then:
your position = position of the bus
1/2 a * t² = x0 + v * t
1/2 * 0.960 m/s² * t² = 11.0 m + 5.00 m/s * t
0.48 m/s² * t² - 5.00 m/s * t - 11.0 m
Solving the quadratic equation:
t = 12.3 s
Using t = 12.3 in the equation of your position, we will obtain the distance you have to run to catch the bus:
x = 1/2 * 0.960 m/s² * (12.3 s)² = 72.6 m
B) The equation for velocity is:
v = v0 + a * t
Since you start from rest, v0 = 0. Then, the velocity when you reach the bus at t = 12.3 s will be:
v = a * t
v = 0.960 m/s² * 12.3 s = 11.8 m/s
C) The velocity you have to run is almost the world record of Usain Bolt (45 km / h).
11.8 m/s *(3600 s/ h) *( 1 km / 1000 m) = 42.5 km/h.
Then, no, an average college student would not be able to run that fast.
