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Motion in Straight Line
Question
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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)2 

(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)2 

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

Answer

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.

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Some More Questions From Motion in Straight Line Chapter

Can a train be taken a particle? Give an example in support of your answer.

 A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion: 

(a) A kite flying in the sky.

(b) The earth revolving around the sun. 

(c) A train moving along the equator of the earth in clockwise direction. 

(d) Accelerated motion of a particle in a straight line.

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