Speed and acceleration - running for the bus

In summary, a bus with an acceleration of 0.75 m/s^2 and a girl with a constant speed of 8.0 m/s and starting 17.5 m behind the bus will meet when their distances are equal. Using the equations v=v_0+at and s=v_0t+1/2at^2, the time it takes for the girl to catch up with the bus can be found by equating their distances and solving for the time variable.
  • #1
mstud
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0

Homework Statement



A bus goes from the bus stop with the acceleration 0.75 m/s^2. A girl runs after the bus. She has the speed 8.0 m/s, and she was 17.5 m behind the bus as it started.

a) How long time does it take the girl to catch up with the bus?

Homework Equations



THe equations for constant acceleration [itex]v=v_0 +at[/itex] and [itex]s=v_0 t + \frac 12 at^2[/itex]

The Attempt at a Solution



I only came as far as to figure out which variables I have for each object:

BUS: [itex]v_0=0 m/s[/itex]since the bus has no speed at the stop, a=0.75m/s^2

GIRL: [itex]v_0=v=8.0 m/s[/itex] Velocity at start is equal to velocity later when the speed is konstant, a=0m/s^2 No acceleration when an object has constant speed. [itex]s_0=-17.5 m[/itex] Starting point 17.5 m behind the bus

However I can't figure out how to use these variables and formulas to get the time it takes her to catch up with the bus...

Please help!
 
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  • #2
Write an equation for the position with respect to time for each of them. They meet when their distances are equal, so equate the two and solve for the time variable.
 
  • #3
I just found that was the way I could solve it :smile: Many thanks for your help, anyway.
 

1. How is speed and acceleration calculated when running for the bus?

Speed is calculated by dividing the distance traveled by the time it took to cover that distance. Acceleration is calculated by dividing the change in velocity by the time it took to make that change. In the context of running for the bus, speed and acceleration can be calculated by measuring the distance traveled and the time it took to reach the bus stop.

2. What factors affect speed and acceleration when running for the bus?

Several factors can affect speed and acceleration when running for the bus. These include the distance to the bus stop, the individual's fitness level, the terrain, and any obstacles or barriers that may slow down or speed up the runner.

3. How does running for the bus differ from other forms of running in terms of speed and acceleration?

Running for the bus is typically a short burst of running, whereas other forms of running may involve longer distances and different types of terrain. This can affect the speed and acceleration as the runner may need to pace themselves differently and adjust for potential obstacles in their path.

4. How does speed and acceleration affect the likelihood of catching the bus?

Generally, a higher speed and acceleration will increase the chances of catching the bus. However, other factors such as the distance to the bus stop and the bus's speed can also play a role. Additionally, the individual's running technique and physical abilities may also impact their chances of catching the bus.

5. Can speed and acceleration be improved for running for the bus?

Yes, speed and acceleration can be improved through regular exercise, proper running technique, and overall fitness. By incorporating interval training and other forms of cardio into a workout routine, individuals can increase their speed and acceleration, making it easier to run for the bus when needed.

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