Two objects two differents accelerations

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In summary, the conversation was focused on solving a physics problem involving a person running to catch a moving bus. The participants discussed using equations to determine the distance and time at which the person would catch the bus. They also considered the bus's acceleration and the distance between the person and the bus at different times. Eventually, they found that solving for x and t in equations for the runner and the bus would lead to the solution.
  • #1
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I know this is a repost but i need this for tomorow morning so id greatly appreciate it if someone could help me out, thanks a bunch!

Homework Statement



A personne walking at a speed of 1.7m/s see's a stopped bus 25m from him. At this moment this person starts to run with an acceleration of 1,3m/s2. After 4 secondes this personne has reached his maximum speed et it stays constant, but at the same time the bus starts moving and accelerates 2,6m/s2.

Does this person suceed in catching the bus? If so, at what time and at what distance, if not what was the smallest distance between the person and the bus.

- I am sorry if there any mistakes, i translated from french.


Homework Equations



Thats my problem i don't know what equations takes into account two moving objects


The Attempt at a Solution



Ive got this so far:

Alright well, by using the initiale speed of 1,7m/s and 4s, i found his constante speed of 6.9m/s. So after that i used the acceleration and his speed to determine the distance he travelled, 17,2m. i subtracted 17,2m from 25m, which left 7,8m between the bus and the person. Then I am stuck, how do i incorporate both speeds in one equations to see if he caught the bus or not?

Update, i tryed using a time of 8s for both the peron and the bus, and i see that the bus is goin faster then the person and has traveled a greater distance, the only problem is don't know what has happened between 4s and 8s, I am completely lost
 
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  • #2
You first need to find the distance he traveled before his speed was constant.

Once you find that distance then find the relative distance between him and the bus as a function of time. He travels at some constant speed v*t towards the bus which closes the gap while the bus moves away at the speed of 1/2 a*t^2.

Ignoring the movement of the bus for a moment the distance between the runner and the bus is decreasing at the rate of v*t.

Ignoring the movement of the person for a moment the bus is moving at a distance of 1/2 a*t^2 away from the person, thus increasing the distance.

Combining these we have the total distance is the distance between the bus and the person at time 0. Plus the distance the person is traveling. Minus the distance the bus is traveling.

What we end up with is a quadratic function that looks like: D = d - v*t + 1/2 a*t^2. Where 'd' is the distance between the bus and the person at time t = 0 (actually the fourth second of the problem but the zeroth of the equation) and v is the velocity of the person, and a is the acceleration of the bus.
 
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  • #3
This is a tough problem and you will need to solve equations.

One approach is to assume that the runner catches the bus at x metres from the point it was stopped, in time t after it started. Now you can write an equation in x and t for runner and for the bus. If the runner can catch the bus, you will be able to solve for x and t from the two equations. If the runner can't catch the bus, the equations will have no finite solutions.

For the bus the equation is

x = 1/2 (2.6) t^2

try and write the same thing for the runner.
 
  • #4
Thank you sooooo much, that simple little question has been driving me insane, thanks again!

nick
 

1. What is the difference between acceleration and velocity?

Acceleration refers to the rate at which an object's velocity changes over time, while velocity is the speed and direction of an object's motion.

2. How do you calculate acceleration?

Acceleration can be calculated by dividing the change in velocity by the change in time, or by using the formula a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. Can two objects have different accelerations?

Yes, two objects can have different accelerations if they are experiencing different forces or if they have different masses. Acceleration is dependent on the net force acting on an object and its mass.

4. How does air resistance affect the acceleration of two objects?

Air resistance can affect the acceleration of two objects differently depending on their shape, size, and mass. In general, air resistance will slow down the acceleration of an object by creating a drag force that is opposite to the direction of motion.

5. What is the significance of studying two objects with different accelerations?

Studying two objects with different accelerations can help us understand the relationship between force, mass, and acceleration. It also allows us to explore the effects of external factors, such as air resistance, on an object's acceleration. This knowledge is crucial in many fields of science, including physics, engineering, and astronomy.

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