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A distanceтАУtime graph for uniform motion must pass through ________.
(0,1)
(1,1) only
Any point
The origin
The origin
Remember that uniform motion signifies a straight-line graph starting from rest. At time t=0, distance s must be 0, which corresponds to the coordinates (0,0).
Uniform motion implies that the velocity of the body is constant over time, and at the starting time t=0, the displacement is zero.
s=v├Чt
Remember that uniform motion signifies a straight-line graph starting from rest. At time t=0, distance s must be 0, which corresponds to the coordinates (0,0).
Students often confuse the y-intercept of a non-zero initial position (where the graph would start at some s>0) with the general definition of uniform motion.
Define Uniform Motion
Uniform motion is defined by constant speed or velocity, meaning equal distances are covered in equal intervals of time.
v=╬Фt╬ФsтАЛ=constant
Establish Mathematical Model
The linear relationship between distance (s) and time (t) is represented by the equation s=vt+c. For pure uniform motion starting from a stationary position, the initial displacement is zero.
s(t)=vтЛЕt+s0тАЛ
Coordinate Geometry Analysis
If the object is at the starting point (origin) at t=0, then s(0)=0. This implies the line must pass through the origin (0,0).
(t,s)=(0,0)
D is correct because uniform motion starting from rest mathematically implies that at t=0, distance s=0, which is the origin (0,0) on a Cartesian plane.
This concept is fundamental to understanding velocity-time graphs as well, where the area under the curve represents total displacement.
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