A car moving at constant speed of 30m/s suddenly stalls at the bottom of a hill.

Question

A car moving at constant speed of 30m/s suddenly stalls at the bottom of a hill. The car undergoes a constant acceleration of -2m/s2 while ascending the hill. 1. Write equations for the position and the velocity as a function of time, taking x=0 at the bottom of the hill where vo = 30m/s. 2. Determine the maximum distance traveled by the car up the hill after stalling. A student throws a set of keys vertically upward to another student in a window 4m above as in Figure 2.6. The keys are caught 1.5s later by the student. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

Explanation / Answer

vo = 30 m/s, a = -2 m/s^3

1) from kinematic equations

x = vot+0.5at^2

x = 30t -0.5*2*t^2

x = 30t - t^2

v = vo +at

v = 30 -2t

2) from kinematic equaitons

v^2 - vo^2 = 2as

0 - 30^2 = -2*2*s

s = 225 m

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