Question

Identical objects, Object X and Object Y, are tied together by a string and placed at rest on an incline, as shown in the figure. The distance between the
center of mass of each object is 2 m. The system of the two objects is released from rest, and a graph of the system's center of mass velocity as a
function of time is shown. Based on the data, approximately how much time will it take the center of mass of Object X to reach point J near the bottom
of the incline?

Answer 1

The slope of the velocity time graph of an object moving with constant acceleration is constant

It will take approximately 3 seconds for the center of mass of Object X to reach point J near the bottom of the incline

The reason why the above time value is correct is given as follows:

Known parameters:

Initial velocity of the objects, u = 0

The graph  in the question is a straight line graph with data points

(0, 0), (0.5, 1.0), (1.0, 2), (3.0, 6), and (3.5, 7)

Given that the slope of the velocity-time graph is constant, we have that the acceleration is constant and is given as follows;

$a = \dfrac{\Delta v}{\Delta t } = \dfrac{v_2 - v_1}{t_2 - t_1}$

Therefore;

$a = \dfrac{6 - 2}{3.0 - 1.0} = 2$

The acceleration, a ≈ 2 m/s²

The distance from the center of mass of the Object X to the point J near the bottom = 9 m

The equation for distance travelled is given as follows;

$s = u\cdot t + \dfrac{1}{2} \cdot a \cdot t^2$

Which gives;

$9 = 0\times t + \dfrac{1}{2} \times 2 \times t^2 = t^2$

t = √9 = 3

The time it will take the center of mass of Object X to reach point J near the bottom of the incline is t = 3 seconds

Learn more about motion under constant acceleration here:

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