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:
And substituting this into the displacement equation:
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: