How to calculate vehicle deceleration (time to stop)

[sparknote_s]

Ok here is my question. Take a person riding a bike. If you can calculate their momentum by knowing their total weight and speed, how could you calculate the DISTANCE they will roll if they stop pedalling and apply no force. Assume that there is absolutely no wind at the time. And add in a grade to the road, expressed in vertical distance divided by road length (hypotenuse of triangle).

What equations would you use, and how would you calculate it?

Thanks.

 

[dextercioby]

Well,if it's climbing up an incline,you can use simple kinematics.If the wheels are rolling and there's no friction,i assume the tangential component of gravity will slow the bike down to eventual stopping.

So simply use the kinematics on an incline.

Daniel.

 

[thepatientmental]

To calculate the distance a person riding a bike will roll if they stop pedaling and apply no force, we can use the equation for deceleration: a = (vf - vi)/t, where a is the deceleration, vf is the final velocity (in this case, 0 m/s), vi is the initial velocity (the speed at which the person is riding the bike), and t is the time it takes for the person to come to a complete stop.

To find the time, we can use the equation t = (vf - vi)/a, where t is the time, vf is the final velocity (0 m/s), vi is the initial velocity, and a is the deceleration.

Next, we can use the equation d = vi*t + 1/2*a*t^2, where d is the distance, vi is the initial velocity, t is the time, and a is the deceleration.

To incorporate the grade of the road, we can use the equation d = vi*t + 1/2*a*t^2 + (g*sinθ*t^2)/2, where d is the distance, vi is the initial velocity, t is the time, a is the deceleration, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the grade in radians.

By plugging in the given values for weight, speed, and grade, we can solve for the distance the person will roll before coming to a complete stop. It is important to note that this calculation assumes that there is no friction or external forces acting on the person and bike, and that the person is coming to a complete stop without any additional movements or actions.