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How do you know there is no motion on a distance time-graph?
distance = velocity x time so on the graph velocity is slope. If slope is zero (horizontal line) there is no motion
What does a zero slope look like?
in a graph, a line with a zero slope is the one that is parallel to the x-axis. It is represented by an equation of the form y = a constant, independent of x values.
Derivative of zero?
The derivate of zero - as well as the derivative of ANY constant (non-variable) number, is zero. (A graph of y = 0 for example will be a horizontal line - the slope is zero.)
When the value of the slope gets smaller the graph of a line gets?
less steep (apex)
How would a graph of negative and positive acceleration differ?
This depends on what the graph represents. If it is a graph of velocity on the vertical and time on the horizontal, then if acceleration is at a constant rate, the graph will be a straight line with positive slope (pointing 'up'). If acceleration stops, then the graph will be a horizontal line (zero acceleration or deceleration). If it is deceleration (negative acceleration), then the graph will have negative slope (pointing down).
