Name: Motion on an Inclined Plane
Uploaded: 2019-07-19
Duration: 6 min 34 s
Description: We all are curious about gravity. Through this video, let us learn to break the force of gravity into components in case of motion on an inclined plane.

Question

Show that for the motion of uniform velocity, the slope of the time-displacement graph is equal to the velocity of the object. What do you understand by negative value of velocity? Explain it by an example.

Accepted Answer

If we measure the displacements with respect to some reference point of a moving object at different times and draw a graph between time and displacement, then it is called a 'time-displacement graph'.

If we draw a graph taking time along $X$ axis and displacement along $Y$ axis, then it will be as shown. Since the graph is a straight line, it expresses that the moving object is being displaced equally in equal limes. In other words, the object is moving with a 'uniform’ velocity, that is, its average velocity and instantaneous velocity are the same.

If the time-displacement graph of a moving object is a straight line, then the slope of this line with the $X$ axis gives the velocity of the object. For this, two points, $A$ and $B$ are taken on the straight line. Let $t_{1}$ be the time and $s_{1}$ , the displacement corresponding to the point $A$ and $t_{2}$ and $s_{2}$ , corresponding to the point $B$ . Clearly, the object is displaced from $s_{1}$ to $s_{2}$ between the times $t_{1}$ and $t_{2}$ . The velocity of the object is,

$v = \frac{D i s p l a c e m e n t}{T i m e i n t e r v a l} = \frac{s_{2} - s_{1}}{t_{2} - t_{1}} = \frac{∆ s}{∆ t}$

But, $\frac{∆ s}{∆ t} = \frac{C B}{A C}$

Thus, $v = \frac{C B}{A C}$

It follows that the velocity of uniform motion equals the slope of the time-displacement graph.

Negative velocity just means velocity in the opposite direction than what would be positive. An object which moves in the negative direction has a negative velocity.

For example, If a person drive from home to school (defining this a positive direction), then velocity of the person is positive, but negative when the same person go home from school. It is all about direction seen from how the person defined its positive axis.

Show that for the motion of uniform velocity, the slope of the time-displacement graph is equal to the velocity of the object. What do you understand by negative value of velocity? Explain it by an example.

Important Questions on Motion in One and Two Dimensions

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