How is constant acceleration represented on a velocity time graph

Asked by admin @ 28/10/2021 in Physics viewed by 357 People

Assume this is an acceleration graph, where the X axis represents time in seconds and the Y axis represent velocity in m/s. Which statement BEST describes the acceleration represented by the graph?

A)There is no acceleration.
B) Acceleration is positive.
C) Acceleration is positive and constant.
D) Acceleration is positive and increasing.

Answered by admin @ 28/10/2021

Answer:

D) Acceleration is positive and increasing.

Explanation:

Acceleration is defined as the rate of change of velocity per unit time; in formulas:

$a=\frac{\Delta v}{\Delta t}$

where $\Delta v$ is the variation of velocity and $\Delta t$ is the variation in time.

The graph shows the velocity vs the time of a moving object. We can see that $\Delta v$ is the increment on the y-axis, while $\Delta t$ is the increment on the x axis: therefore, the ratio $\frac{\Delta v}{\Delta t}$ is the slope of the curve. In fact, in a velocity-time graph, the slope of the curve corresponds to the acceleration of the object.

In this particular graph, we see that the slope of the curve continues to increase: therefore, the acceleration is positive (because the slope is positive, since the velocity is increasing) and increasing (because the slope is increasing).

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