Acceleration Direction Determines Its Sign
The sign of acceleration (positive or negative) depends on the chosen coordinate system and the direction of acceleration relative to the direction of velocity.
We typically define a positive direction. If the velocity is in this positive direction:
- If acceleration is also in the same (positive) direction, it increases the speed. In this case, acceleration is considered positive.
- If acceleration is in the opposite (negative) direction, it decreases the speed. In this case, acceleration is considered negative.
Conversely, if the velocity is in the negative direction, the interpretation flips, but the core principle remains: acceleration in the direction of velocity increases speed (positive relative to velocity), and acceleration opposite to velocity decreases speed (negative relative to velocity).
Correct Answer Justification
Option A correctly states this relationship: "Acceleration is positive if it is in the direction of velocity, and negative if it is opposite." This aligns with the standard convention where acceleration contributing to increased speed (in the direction of motion) is positive, and acceleration causing deceleration is negative, assuming velocity is initially in the positive direction.
Important Questions from Acceleration
Acceleration is equal to the rate of change of _________.
At uniform speed the acceleration is
At uniform speed the acceleration is
- If the position of a particle X at time $t$ is given by the equation $x(t) = At^3$, where $A$ is a non-zero constant, determine the nature of its acceleration.
- Which of the following mathematical expressions accurately defines the average acceleration, $a$, of an object that changes its velocity from an initial velocity $v_i$ to a final velocity $v_f$ during a time interval $t$?
