Question

1. describe the acceleration of the object shown in the velocity vs. time graph below.

graph with x-axis (-10 to 10), y-axis (-10 to 10), line passing through (-3,6), (0,3), (3,0)
option: the object has a positive acceleration

Explanation:

Answer:

To determine acceleration from a velocity - time graph, we use the formula for the slope of the line, since acceleration \(a=\frac{\Delta v}{\Delta t}\) (the slope of the velocity - time graph).

We can use two points on the line, for example, \((x_1,y_1)=(- 3,6)\) and \((x_2,y_2)=(0,3)\) or \((0,3)\) and \((3,0)\).

Using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), if we take \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(3,0)\):

\(m=\frac{0 - 3}{3-0}=\frac{-3}{3}=- 1\)

Since the slope of the velocity - time graph is negative, the acceleration is constant and negative. So the object has a constant negative acceleration (or deceleration in the positive direction context, but strictly from the slope, acceleration is - 1 unit of velocity per unit of time and is constant).

If we were to choose the other option (the one not saying positive acceleration), the correct description is that the object has a constant negative acceleration (or we can say the acceleration is \(- 1\) (with appropriate units) and is constant as the graph is a straight line, so acceleration does not change).