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One-Dimensional Kinematics with Constant Acceleration
Learning Goal:
To understand the meaning of the variables that appear in the equations for one-
dimensional kinematics with constant acceleration.
Motion with a constant, nonzero acceleration is not uncommon in the world around us. Falling (or
thrown) objects and cars starting and stopping approximate this type of motion. It is also the type of
motion most frequently involved in introductory kinematics problems.
The kinematic equations for such motion can be written as
,
,
where the symbols are defined as follows:
is the position of the particle;
is the
initial
position of the particle;
is the velocity of the particle;
is the
initial
velocity of the particle;
is the acceleration of the particle.
In anwering the following questions, assume that the acceleration is constant and nonzero:
.
Part A
The quantity represented by
is a function of time (i.e., is not constant).
ANSWER:
true
false

One-Dimensional Kinematics with Constant Acceleration
Part A
Correct
Part B
The quantity represented by
is a function of time (i.e., is not constant).
ANSWER:
Correct
Recall that
represents an initial value, not a variable. It refers to the position of an object at some
initial moment.
Part C
The quantity represented by
is a function of time (i.e., is not constant).
ANSWER:
true
false
Correct
Part D
The quantity represented by is a function of time (i.e., is not constant).
ANSWER:

One-Dimensional Kinematics with Constant Acceleration
Part C
Correct
The velocity always varies with time when the linear acceleration is nonzero.
Part E
Which of the given equations is not an explicit function of and is therefore useful when you don't
know or don't need the time?
ANSWER:
Correct
Part F
A particle moves with constant acceleration . The expression
represents the particle's
velocity at what instant in time?
ANSWER:

Part E
Correct
More generally, the equations of motion can be written as
and
.
Here
is the time that has elapsed since the beginning of the particle's motion, that is,
,
where is the current time and
is the time at which we start measuring the particle's motion. The
terms
and
are, respectively, the position and velocity at
. As you can now see, the equations
given at the beginning of this problem correspond to the case
, which is a convenient choice if
there is only one particle of interest.
To illustrate the use of these more general equations, consider the motion of two particles, A and B.
The position of particle A depends on time as
. That is, particle A starts
moving at time
with velocity
, from
. At time
, particle B has twice the
acceleration, half the velocity, and the same position that particle A had at time
.
Part G

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