A body is accelerated continuously. What is the form of the graph?
A.
cubic
B.
inverse
C.
linear
D.
quadratic
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The answer is D, quadratic.
a is time rate of change of velocity
a is constant here
so the slope of x VELOCITY versus time is constant
if the slope of velocity versus time is constant
the displacement curve, X VERSUS t, is quadratic
a is constant here
so the slope of x VELOCITY versus time is constant
if the slope of velocity versus time is constant
the displacement curve, X VERSUS t, is quadratic
if you know any calculus
d^2x/dt^2 = a
then
v = dx/dt = a t + constant (strraight line)
then if
dx/dt = v = a t + Vi
then
x = (1/2) a t^2 + Vi t + Xi , parabola, quadratic
d^2x/dt^2 = a
then
v = dx/dt = a t + constant (strraight line)
then if
dx/dt = v = a t + Vi
then
x = (1/2) a t^2 + Vi t + Xi , parabola, quadratic
Xi is position when t = 0
and
Vi is velocity when t = 0
and
Vi is velocity when t = 0
The answer is B.
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