Question

When you draw a velocity-time graph and use the area under it to find the change in position (displacement), what kind of shortcut applies to determine acceleration?

A) There is no easy shortcut.
B) It indicates positive acceleration.
C) It indicates negative acceleration.
D) It indicates zero acceleration.

Answer 1

The gradient of the velocity-time graph is the shortcut for determining acceleration; a positive slope indicates positive acceleration, a negative slope indicates negative acceleration, and a zero slope indicates zero acceleration.

Step-by-step explanation:

When considering a velocity-time graph in physics, the gradient (slope) of the velocity-time graph represents the acceleration of the object in motion. Therefore, the correct shortcut when analyzing a velocity-time graph to determine acceleration is the gradient of the graph.

For example, if the graph shows a straight line with a positive slope, this indicates positive acceleration; a negative slope indicates negative acceleration, and a flat line (a slope of zero) indicates zero acceleration. Hence, regarding the options provided for the shortcut that applies to determine acceleration:

• B) It indicates positive acceleration, is true if the slope is positive.
• C) It indicates negative acceleration, is true if the slope is negative.
• D) It indicates zero acceleration, is true if the slope is zero.

However, it is important to note that option A) There is no easy shortcut, is not correct since the gradient of the velocity-time graph is a straightforward method for determining acceleration.