Help Solving Motorcycle Braking Problem | Reaction Time, Acceleration, Distance

[ConnorPhys]

A motorcyclist sees an obstacle and comes to a complete stop. Given are reaction time (0.8seconds), acceleration once started braking (-6.5meters/seconds^2), and total distance traveled (35meters) from initial sighting to complete stop. Solve to find initial velocity and time from when he started braking to when he stopped.

I can't figure out a single formula to use that will help me find one of the unknowns and solve the problem! Please help!

 

[haruspex]

You must know some equations relating to uniform acceleration. (The acronym SUVAT is often used.)

 

[NascentOxygen]

A motorcyclist sees an obstacle and comes to a complete stop. Given are reaction time (0.8seconds), acceleration once started braking (-6.5meters/seconds^2), and total distance traveled (35meters) from initial sighting to complete stop. Solve to find initial velocity and time from when he started braking to when he stopped.

I can't figure out a single formula to use that will help me find one of the unknowns and solve the problem! Please help!

Neither can I ! Certainly not until I have first condensed the wordy problem sentences into a familiar mathematical form, e.g.,

v_f = 0 m/sec
reaction time t = 0.8 secs
total distance d = 35m
...

v_i = ?? m/sec

That done, the next step is to write down all the equations of motion that you know. Then go through them one by one, ticking off the variables you know or need, until you have highlighted by multiple ticks some likely candidates to use for solving this.

 

[willem2]

Suppose you did know the speed of the motor cyclist. call it v. Could you compute the distance traveled during the reaction time, and the distance traveled when breaking?
Set the stopping distance equal to the sum of those two distances and solve for v.

 

[Nickie]

I would approach this problem by first identifying the known variables and their corresponding units. In this case, we know the reaction time is 0.8 seconds, the acceleration is -6.5 meters/seconds^2, and the total distance traveled is 35 meters.

Next, I would use the known equation for distance (d = 0.5at^2 + vt) to solve for the initial velocity (v) and time (t) from when the motorcyclist started braking to when they stopped. This equation can be rearranged to solve for v and t as follows:

v = (d - 0.5at^2)/t

t = √(2d/a)

Plugging in the known values, we get:

v = (35m - 0.5(-6.5m/s^2)(0.8s)^2)/(0.8s) = 7.8m/s

t = √(2(35m)/-6.5m/s^2) = 2.7s

Therefore, the initial velocity of the motorcyclist before braking was 7.8m/s and it took them 2.7 seconds to come to a complete stop.

In conclusion, by using the known equations and values, we were able to solve for the initial velocity and time from when the motorcyclist started braking to when they stopped. It is important to carefully identify and use the appropriate equations in order to accurately solve scientific problems.