A object travels at constant negative acceleration. What does the graph of the object's velocity as a function of time look like?
When an object travels with constant negative acceleration, this means that the acceleration is directed opposite to the object's motion, causing the object to slow down if it's moving forward or speed up if it's moving backward.
A graph of the object's velocity (v) as a function of time (t) would be a straight line with a negative slope. The negative slope indicates that the velocity is decreasing over time at a constant rate. If the object starts with a positive initial velocity, the line would start at a positive value on the y-axis (velocity axis) and slope downward to the right as you move along the x-axis (time axis).
There are three possible scenarios for how the graph could look, depending on the initial velocity (v0) of the object:
1. If v0 > 0 (the object starts moving forward): The graph will start at some positive value on the y-axis and slope downwards to the right. If the negative acceleration is maintained long enough, the line will cross the x-axis (where velocity is zero) and continue into the negative velocity region, indicating that the object has started to move in the reverse direction.
2. If v0 = 0 (the object starts from rest): The graph will start at the origin (0,0) and slope downwards to the right, showing that the object immediately begins to move in the reverse direction, speeding up as time increases.
3. If v0 < 0 (the object starts moving backward): The graph will start at some negative value on the y-axis and slope further down to the right, showing that the object is speeding up in the backward direction.
In all three cases, the key characteristic of the graph will be its straight line with a consistent negative slope, which is indicative of a constant negative acceleration. The actual slope of this line is equal to the magnitude of the acceleration.