Question

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

Explanation:

Step1: Recall the formula for acceleration from a velocity - time graph

Acceleration \(a=\frac{\Delta v}{\Delta t}\), which is the slope of the velocity - time graph. The formula for the slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Identify two points on the graph

We can use the points \((- 3,6)\) and \((0,3)\). Here, \(x_1=-3,y_1 = 6,x_2 = 0,y_2=3\).

Step3: Calculate the slope (acceleration)

Substitute the values into the slope formula:

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Since the slope of the velocity - time graph is constant, the acceleration is constant. The negative sign indicates that the acceleration is in the opposite direction of the positive velocity direction.

Answer:

The object has a constant acceleration of \(-1\space unit\) (the negative sign implies it is decelerating if we assume the initial positive velocity direction as the reference for motion).