Textbook Question
At this instant, the particle is speeding up and curving upward. What is the direction of its acceleration?
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2. 1D Motion / Kinematics
Intro to Acceleration
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At a given instant, the acceleration of a certain particle is zero. This means that:
A
the velocity is not changing at that instant.
B
the velocity is increasing.
C
the velocity is decreasing.
D
the velocity is zero.
Verified step by step guidance1
Understand the relationship between acceleration and velocity: Acceleration is the rate of change of velocity with respect to time. If acceleration is zero, it means there is no change in velocity at that instant.
Consider the definition of acceleration: Mathematically, acceleration \( a \) is defined as \( a = \frac{dv}{dt} \), where \( v \) is velocity and \( t \) is time. If \( a = 0 \), then \( \frac{dv}{dt} = 0 \).
Interpret the mathematical expression: \( \frac{dv}{dt} = 0 \) implies that the derivative of velocity with respect to time is zero, meaning velocity is constant at that instant.
Clarify the implications: A constant velocity means that the velocity is not increasing or decreasing; it remains the same.
Conclude the reasoning: Therefore, when the acceleration is zero, the correct interpretation is that the velocity is not changing at that instant.
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