An vehicles starts from rest and accelerates at a rateof 2m/s 2 in a straight li

Question

An vehicles starts from rest and accelerates at a rateof 2m/s2 in a straight line until it reaches a speed of20m/s. The vehicle then slows at a constant rate of1m/s2 until it stops. a. What is the total time for the trip,from the start to thestop? b. How far does the vehicle travel from start to stop? An vehicles starts from rest and accelerates at a rateof 2m/s2 in a straight line until it reaches a speed of20m/s. The vehicle then slows at a constant rate of1m/s2 until it stops. a. What is the total time for the trip,from the start to thestop? b. How far does the vehicle travel from start to stop?

Explanation / Answer

Initial speed u = 0

Acceleration a = 2 m / s ^ 2

Final speed v = 20 m / s

Time taken to reach 20 m/ s speed is t = ( v – u 0 /a

                                                              = 10 s

Distance travel in this time t is S = ut + ( 1/ 2) at^2

                                                       = 0 + 100 m = 100 m

Stage (2) :

Initial velocity U = v = 20 m / s

Final velocity V = 0 m / s

Acceleration a’ = -1 m / s ^ 2

Time t ‘ = [ V –U ] / a ‘

               = 20 s

Distance travel in this time S ‘ = Ut ‘ + ( 1/2) a ‘t ‘^ 2

                                                 = 400 – 200 = 200 m

(a). total time T = t + t ‘ = 30 S “ = S + S ‘= 300 m

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