What is the least time to get from point ##A## to point ##B##

In summary, the conversation discusses finding the distance and time taken for a cyclist to come to a stop after decelerating from a speed of 12 m/s for 4 seconds. The equation v=u+at is used to calculate the distance travelled, which is found to be 24 m. The time taken to come to a complete stop is then found to be 22 seconds. The conversation also mentions an alternative approach using a velocity vs. time graph and points out some issues with the given equations.
  • #1
chwala
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Homework Statement
A cyclist travels from point ##A## to ##B##, a distance of ##240## metres. He passes ##A## at ##12## m/s, maintains this speed for as long as he can, and then breaks so that he comes to a stop at ##B##. If the maximum deceleration he can achieve when braking is 3 m/s^2, what is the least time in which he can get from ##A## to ##B##?
Relevant Equations
Velocity and acceleration
My approach;

##v=u+at##

##0=12-3t##

##t=4##

i.e at point when deceleration starts up to the point cyclist stopped (point ##B##).

Therefore, distance travelled in the ##4## seconds is given by,

##s=(12×4)+(0.5×-3×16)=48-24=24##m

##⇒240-24=216##m

##t=\dfrac{216}{12}=18 ##seconds.

Therefore least time taken is ##4+18=22## seconds.

Text book has only given the answer ##22##

your insight or alternative approach is welcome.
 
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  • #2
Your approach is correct and I would have done it the same way.

Two things I don't appreciate: the lack of units in the intermediate equations and the fact that you have not stated the equation for ##s## you are using. Also ##0.5 \times -3 \times 16## is not proper mathematics, that should be ##0.5 \times (-3) \times 16##.
 
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  • #3
Try analyzing the cyclist's motion using a velocity vs. time graph.
 
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1. What factors affect the least time to get from point A to point B?

The least time to get from point A to point B is affected by several factors, including the distance between the two points, the mode of transportation, the route taken, and any potential obstacles or delays along the way.

2. How do you calculate the least time to get from point A to point B?

The least time to get from point A to point B can be calculated by dividing the distance between the two points by the speed of the chosen mode of transportation. This calculation may also need to take into account any potential delays or obstacles along the way.

3. Is there a universal least time to get from point A to point B?

No, the least time to get from point A to point B is not universal and can vary depending on the factors mentioned above. It is also influenced by external factors such as weather conditions and traffic.

4. How can the least time to get from point A to point B be minimized?

The least time to get from point A to point B can be minimized by choosing the most efficient mode of transportation, taking the shortest route, and avoiding potential obstacles or delays. Advanced planning and using real-time traffic or navigation apps can also help minimize travel time.

5. Can the least time to get from point A to point B be accurately predicted?

While the least time to get from point A to point B can be estimated based on factors such as distance and mode of transportation, it is difficult to accurately predict due to external factors and unforeseen circumstances. However, with advanced technology and data analysis, the accuracy of these predictions is constantly improving.

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