Page 48 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 3] MOTION IN A STRAIGHT LINE 33

s 270 km
(a) ¯ v = = = 60 km/h
t 4.5h
(b) s = ¯vt = (60 km/h)(7.0h) = 420 km
s 300 km
(c) t = = = 5.0h
¯ v 60 km/h

SOLVED PROBLEM 3.5

An airplane whose velocity relative to the air is a constant 800 km/h has a constant tailwind of 240 km/h.
How long will it take the airplane to cover 2000 km relative to the ground?
The ground velocity of the airplane is

v = 800 km/h + 240 km/h = 1040 km/h
Hence the time needed to cover 2000 km over the ground is
s 2000 km
t = = = 1.92 h = 1h55 min
v 1040 km/h

SOLVED PROBLEM 3.6
A car travels at 100 km/h for 2 h, at 60 km/h for the next 2 h, and finally at 80 km/h for 1 h. What is the
car’s average velocity for the entire journey?
The car’s average velocity equals the total distance it covers divided by the total time. Hence
s 1 + s 2 + s 3 v 1 t 1 + v 2 t 2 + v 3 t 3
¯ v = =
t 1 + t 2 + t 3 t 1 + t 2 + t 3
(100 km/h)(2h) + (60 km/h)(2h) + (80 km/h)(1h)
=
2h + 2h + 1h
400 km
= = 80 km/h
5h

ACCELERATION
Abodywhosevelocityischangingisaccelerated.Abodyisacceleratedwhenitsvelocityisincreasing,decreasing,
or changing in direction. Accelerations that involve a change in direction are discussed in Chapter 9.
The acceleration of a body is the rate at which its velocity is changing. If a body moving in a straight line
has a velocity of v 0 at the start of a certain time interval t and of v at the end, its acceleration is
v − v 0
a =
t
velocity change
Acceleration =
time
A positive acceleration means an increase in velocity; a negative acceleration (sometimes called a deceleration)
means a decrease in velocity. Only constant accelerations are considered here.
The defining formula for acceleration can be rewritten to give the final velocity v of an accelerated body:

v = v 0 + at
Final velocity = initial velocity + (acceleration)(time)