- The acceleration is equal to the slope of the velocity-versus-time graph.
Although this graph is not composed of straight lines, the concept of slope still
applies; at each point, the slope of the curve is the slope of the tangent line to
the curve. The slope is essentially zero at points A and D (where the curve is
flat), small and positive at B, and small and negative at E. The slope at point C
is large and positive, so this is where the object’s acceleration is the greatest.
- If the graph shown were a position-versus-time graph, then the slope
would be equal to the velocity. The slope of the given graph starts at zero
(around point A), slowly increases to a small positive value at B, continues to
slowly increase to a large positive value at C, and then, at around point D,
quickly decreases to zero. Of the points designated on the graph, point D is the
location of the greatest slope change, which means that this is the point of the
greatest velocity change. Therefore, this is the point at which the magnitude of
the acceleration is greatest.
One Slope to Rule
Them All
The greater the slope at a
point on a velocity-vs-time
graph, the greater the
acceleration.
The greater the slope at a
point on a position-vs-time
graph, the greater
the velocity.
