Now we will solve numerical the example:
Step 1 we found that d_{ca} = 212.67 m and d_{ma} = 72.34 m
Step 2 Find the values of t_{ca} and t_{ma}
Because d_{ca} < D 
we have t_{ca} = v_{c} / a_{c} = 14.58 s 
Because d_{ma} < D 
we have t_{ma} = v_{m} / a_{m} = 3.47 s 
Step 3 Find the values of d_{c} = 787.33 m and d_{m} = 927.66 m
Step 4 Find the values of t_{c} = 27 s and t_{m} = 22.26 s
Step 5 Calculate the values of T_{c} = 41.58 s and T_{m} = 40.73 s
Step 6 Because T_{c} > T_{m} the motorcycle will win the race.
Now we will calculate the distance that the car did:
Because T_{m} = 40.73 s and t_{ca} = 14.58 s we have:
T_{m} > t_{ca} therefore d_{car} = 975.46 m
Notes: there are four possible schemes for the car and the motorcycle acceleration and steady speed motion that has to be analysed in order to solve the problem.
Note: Motorcycle delay time is positive, car delay time should be negative value  Ex5. *** all the results values are in [m] and [s].
