TEST BANK FOR Elementary Mechanics and Thermodynamics By Prof. John W. Norbury

CHAPTER 1. MOTION ALONG A STRAIGHT LINE
1. The following functions give the position as a function of time:
i) x = A
ii) x = Bt
iii) x = Ct2
iv) x = Dcos !t
v) x = E sin !t
where A;B;C;D;E; ! are constants.
A) What are the units for A;B;C;D;E; !?
B) Write down the velocity and acceleration equations as a function of
time. Indicate for what functions the acceleration is constant.
C) Sketch graphs of x; v; a as a function of time.
SOLUTION
A) X is always in m.
Thus we must have A in m; B in msec¡1, C in msec¡2.
!t is always an angle, µ is radius and cos µ and sin µ have no units.
Thus ! must be sec¡1 or radians sec¡1.
D and E must be m.
B) v = dx
dt and a = dv
dt. Thus
i) v = 0 ii) v = B iii) v = Ct
iv) v = ¡!D sin !t v) v = !E cos !t
and notice that the units we worked out in part A) are all consistent
with v having units of m¢ sec¡1. Similarly
i) a = 0 ii) a = 0 iii) a = C
iv) a = ¡!2Dcos !t v) a = ¡!2E sin !t