There is motion of a straight track between two stations.
Average speed: 12m/s
Distance between stations: 3600m.
Please help how could I find the max speed given these information? and it isn't like the average speed so it confused me
Distance = 3600 m
Average Speed = 12 m/s
Time = 3600/12 = 300 sec
You cannot obtain the maximum speed from this information alone, for that you require some information regarding acceleration.
Let us assume that there is a constant acceleration till the the middle of the stations, and from the middle point the vehicle decelerates at the same rate.
So, we can obtain the max speed, which would be at the middle point, by using equations of motion for half the journey.
s = 1800m
t = 150 sec (Since the journey is symmetrical)
s = (1/2)at^2
=> 1800 = (1/2)(a)(150)^2
=> 3600/22500 = a
=> a = 36/225
= 12/69 m/s^2
Now,
v = u + at
=> v = 0 + (12/69)*150
=> v = 1800/69
= 26 m/s
THANK U LOTS!
To find the maximum speed, we need to consider that the average speed is the total distance traveled divided by the total time taken.
In this case, the average speed is given as 12 m/s and the distance between the two stations is 3600 m. So we can calculate the total time taken as follows:
Total Time = Distance / Average Speed
Total Time = 3600 m / 12 m/s
Total Time = 300 seconds
Now, let's consider the case of maximum speed. The maximum speed occurs when the object travels the entire distance in the shortest possible time. In this case, the shortest possible time would be if the object traveled the distance in the same amount of time it took to travel from the first station to the second station at the average speed, but in the opposite direction.
So, to find the maximum speed, we need to calculate the time it takes to travel from the first station to the second station at the average speed and then subtract that time from the total time.
Time from First Station to Second Station at Average Speed = Distance / Average Speed
Time from First Station to Second Station at Average Speed = 3600 m / 12 m/s
Time from First Station to Second Station at Average Speed = 300 seconds
Max Speed = Distance / (Total Time - Time from First Station to Second Station at Average Speed)
Max Speed = 3600 m / (300 seconds - 300 seconds)
Max Speed = 3600 m / 0 seconds
In this case, the maximum speed is undefined because it would imply traveling the entire distance in zero seconds, which is not possible.
Therefore, based on the given information, the maximum speed cannot be determined as the total time is equal to the time required to travel from the first station to the second station at the average speed.