Textbook Question
Show that (see Eq. 2–12d) is not valid when the acceleration , where A and B are non-zero constants.
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2. 1D Motion / Kinematics
Kinematics Equations
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Which of the following statements correctly describes the relationship between displacement, initial velocity, time, and acceleration in kinematics?
A
Displacement is equal to initial velocity plus acceleration multiplied by time.
B
Displacement is equal to initial velocity multiplied by time plus half the acceleration multiplied by time squared.
C
Displacement is equal to initial velocity divided by time plus acceleration.
D
Displacement is equal to initial velocity multiplied by time minus half the acceleration multiplied by time squared.
Verified step by step guidance1
Identify the kinematic equation that relates displacement (s), initial velocity (u), time (t), and acceleration (a). The correct equation is: \( s = ut + \frac{1}{2}at^2 \).
Analyze the given options to see which one matches the correct kinematic equation.
Option 1 states: 'Displacement is equal to initial velocity plus acceleration multiplied by time.' This can be written as \( s = u + at \), which is incorrect as it does not match the kinematic equation.
Option 2 states: 'Displacement is equal to initial velocity multiplied by time plus half the acceleration multiplied by time squared.' This can be written as \( s = ut + \frac{1}{2}at^2 \), which matches the correct kinematic equation.
Option 3 and 4 can be analyzed similarly, but they do not match the correct kinematic equation. Therefore, the correct statement is Option 2.
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