Mean Speed
The area under a velocity-time graph is the distance traveled.
Sample Problems
Example 4
A train moving in a straight line with an initial velocity of 0.50 m/s accelerates at 2.0 m/s^2 for 2.0 seconds, coasts with zero acceleration for 3.0 seconds, and then accelerates at -1.5 m/s^2 for 1.0 seconds. (a) What is the final velocity of the train? (b) What is the average acceleration of the train?
Equations of Constant Acceleration
1. 
2. 
3. 
4. 
Example 5
A ball is thrown straight upward with an initial velocity of +8.2 m/s. If the acceleration of the ball is -9.81 m/s^2, what is its velocity after (a) 0.50 s, and (b) 1.0 s?
Example 6
A drag racer starts from rest and accelerates at 7.40 m/s^2. How far has it traveled in (a) 1.00 s, (b) 2.00 s, and (c) 3.00 s?
Example 7
Jets
at JFK International Airport accelerates from rest at one end of a
runway, and must attain takeoff speed before reaching the other end
of the runway. (a) Plane A has acceleration a and takeoff speed 
.
What is the minimum length of runway, 
,
required for this plane? Give a symbolic answer. (b) Plane B has the
same acceleration as Plane A, but requires twice the takeoff speed.
Find 
and
compare with .
(c) Find the minimum runway length for plane A if a = 2.20 m/s^2 and =
95.0 m/s. (These values are typical for a 747 jetliner.)
Example 8
A park ranger driving on a back country road suddenly sees a deer "frozen" in his headlights. The ranger, who is driving at 11.4 m/s, immediately applies the brakes and slows with an acceleration of 3.80 m/s^2. (a) If the deer is 20.0 m from the ranger's vehicle when the brakes are applied, how close does the ranger come to hitting the deer? (b) How much time is needed for the ranger's vehicle to stop?
Example 8a
The
ranger brakes for 17.1 m to come to rest. After braking for only half
that distance, 8.55 m, is the ranger's speed (a) equal to 
,
(b) greater than ,
(c) less than ?
Example 9
A speeder doing 40.0 mi/hr (about 17.9 m/s) in a 25 mi/hr zone approaches a parked police car. The instant the speeder passes the police car, the police begin their pursuit. If the speeder maintains a constant velocity, and the police car accelerates with a constant acceleration of 4.50 m/s^2, (a) how long does it take for the police car to catch the speeder, (b) how far have the two cars traveled in this time, and (c) what is the velocity of the police car when it catches the speeder?
