Motion in a Straight Line

Question : 28

Total: 27

The velocity-time graph of a particle in one-dimensional motion is shown in figure. 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)+(1∕2)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)+(1∕2) aaverage(t2–t1)

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

Solution:

(a) It is not correct. The reason is that in the time interval betweent1 and t2, the velocity of the particle is not constant (slope of v-t graph isnot same at all points).
(b) It is also not correct for the reason cited in (a).
(c) It is correct.
(d) It is correct.
(e) It is not correct. In the expression, the average acceleration cannot beused.
(f) It is correct.

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