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3. A bus driver forgets to stop at the bus stop. Just as he passes the stop, he begins to decelerate. Five seconds later, the bus is 80 m beyond the stop and has slowed to 10 m/s.

a. Calculate the speed of the bus as it passed the bus stop.

b. What is the deceleration of the bus( assumed to be constant.)

All kinematics problems have 6 variables (Do, Df, Vo, Vf a & t) and 2 equations (Df=1/2*a*t^2+Vo*t+Do and Vf=a*t+Vo). Any time you can identify 4 of the 6 variables you can ALWAYS solve for the other 2!

In this case the variables are: Do=0m (assume this unless the problem indicates otherwise), Df=80m (given), Vo=? (the first answer to the problem), Vf=10m/s (given), a=? (the second answer to the problem) and t=5s (given).

Substituting into the displacement equation:

Df=1/2*a*t^2+Vo*t+Do becomes 80=1/2*a*5^2+Vo*5+0

While the velocity equation:

Vf=a*t+Vo becomes 10=a*5+Vo

Solving the velocity equation for the acceleration:

a=(10-Vo)/5

And substituting this into the displacement equation:

80=1/2*[(10-Vo)/5]*5^2+Vo*5

Solving for the initial velocity:

160=50-5*Vo+10*Vo therefore Vo=22m/s

Substituting this back into the velocity equation the acceleration becomes:

a=(10-22)/5=-2.4m/s

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.