Abody oscillates with simple harmonic motion along the x-axis. its displacement varies with time according to the equation x = 0.5 sin (pt+p/3). the acceleration (in m/s2) of the body at t = 1.0 s is approximately
a. 3.5
b. 49
c. 14
d. 43
e. 4.3

I'll tell you how I look at this, although I may be missing something important.

Position = x(t) = 0.5 sin(pt + p/3)

Speed = position' = x'(t) = 0.5 p cos(pt + p/3)

Acceleration = speed' = position ' ' = x ' '(t) = -0.5 p² sin(pt + p/3)

At (t = 1.0),

x ' '(t) = -0.5 p² sin( 4/3 p )

In order to evaluate this, don't I still have to know what 'p' is ? ?

I don't think it can be evaluated with the information given in the question.