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Motion in Straight Line

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Physics Part I

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
The velocity-time graph of a particle in one-dimensional motion is shown in Fig. 3.29:

Which of the following formulae are correct for describing the motion of the particle over the time-interval t1 to t2 :

(a) x(t2 ) = x(t1) + v (t1) (t2 – t1) +(½) a (t2 – t1)

(b) v(t2 ) = v(t1) + a (t2 – t1

(c) vaverage = (x(t2) – x(t1))/(t2 – t1

(d) aaverage = (v(t2) – v(t1))/(t2 – t1

(e) x(t2 ) = x(t1) + vaverage (t2 – t1) + (½) aaverage (t2 –t1)

(f) x(t2 ) – x(t1) = area under the v-t curve bounded by the t-axis and the dotted line shown.

The correct formulae describing the motion of the particle are (c), (d) and, (f).

The given graph has a non-uniform slope.

Hence, the formulae given in (a), (b), and (e) cannot describe the motion of the particle.

Only relations given in (c), (d), and (f) are correct equations of motion.

What is rest?

When an object does not change its position with time, with respect to it's surroundings. In such a case the object is said to be at rest. 

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. 

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. 

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. 

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.