Motion in Straight Line

Physics Part I

Physics

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Figure 3.25 gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude ? In which interval is the average speed greatest ? Choosing the positive direction as the constant direction of motion, give the signs of v and a in the three intervals. What are the accelerations at the points A, B, C and D?

Acceleration is given by the slope of the speed-time graph.

Since the slope of the given speed-time graph is maximum in interval 2, the average acceleration will be the greatest in this interval.

The height of the curve from the time-axis gives the average speed of the particle.

In the given graph, it is clear that the height is the greatest in interval 3.

Hence, the average speed of the particle is the greatest in interval 3.

The slope of the speed-time graph is positive. Hence, acceleration is positive. Similarly, the speed of the particle is positive in this interval.

The slope of the speed-time graph is negative. Hence, acceleration is negative in this interval. However, speed is positive because it is a scalar quantity.

The slope of the speed-time graph is zero. Hence, acceleration is zero in this interval. However, here the particle acquires some uniform speed. It is positive in this interval.

Points A, B, C, and D are all parallel to the time-axis. Hence, the slope is zero at these points. Therefore, at points A, B, C, and D, acceleration of the particle is zero.

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Is absolute rest or absolute motion possible?

Absolute rest and absolute motion is not possible because there is no point in the universe which is at rest and can be taken as point of reference. The planet Earth is in continuous motion.

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What is motion?

When an object changes it's position with time, with respect to it's surroundings, the object is said to be in motion.

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What is the most essential thing to study the motion of a body?

The most essential thing to study the motion is reference frame. Rest and motion are relative terms. It means that an object in one situation can be in rest but in another situation, the same object will be in motion.

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Can a body be always at rest in some frame?

Yes, a body is always at rest in a frame which is fixed with the body itself.

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