Question

Different velocity-time graph lines are shown, displaying the behavior of multiple race carts along a linear track.

Which description correctly identifies cart C?

A) Has a positive acceleration and is speeding up.
B) Moving with zero acceleration.
C) Moving at a constant acceleration.
D) Has a negative acceleration and is slowing down.

Answer 1

B) Moving with zero acceleration.

Step-by-step explanation:

As we can see the graph for Cart C that its velocity is constant and not changing its magnitude as well as its sign

So here the magnitude and direction is constant so we can say that velocity will remain constant always.

Where we can define the acceleration as

`a = (dv)/(dt)`

so here if magnitude and direction both are constant so

`a = 0`

so we can say that acceleration of cart C is ZERO

so correct answer will be

B) Moving with zero acceleration.

Answer 2

B) Moving with zero acceleration.

Step-by-step explanation:

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

`a=(\Delta v)/(\Delta t)`

In a velocity-time graph, this ratio corresponds to the slope of the curve. In fact:

`\Delta v` (change in velocity) corresponds to the increase in the y-axis

`\Delta t` (change in time) corresponds to the increase in the x-axis

So, acceleration corresponds to the slope of the curve in a velocity-time graph. For cart C, the slope is zero, therefore the acceleration is also zero.