# The velocity-time graph of a particle in one-dimensional motion is shown in Fig. 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)+υ(t1)(t2−t1)+(1/2)a(t2−t1)2 (b) υ(t2)=υ(t1)+a(t2−t1) (c ) υaverage=(x(t2)−x(t1))/(t2−t1) (d) aaverage=(υ(t2)−υ(t1))/(t2−t1) (e ) x(t2)=x(t1)+υaverage(t2−t1)+(1/2)aaverage(t2−t1)2 (f) x(t2)−x(t1)= area under the υ−t curve bounded by the t-axis and the dotted line shown.

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## (c ), (d), (f)

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Updated on:21/07/2023

### Knowledge Check

• Question 1 - Select One

## In any progression, if t2t3t1t4=t2+t3t1+t4=3(t2−t3t1−t4), then t1,t2,t3,t4 are in

AA.P.
BG.P.
CH.P.
Dnone
• Question 2 - Select One

## For any arbitrary motion in space, which of the following relations are true? a) vaverage=(1/2)(v(t1+v(t2) b) vaverage=[r(t2)−rt1t2−t1 v(t)=v(0)+at d) aaverage=[v(t2)−vt1t2−t1 The average stands for average of the quantity over time interval t1 to t_(2)

Avaverage=12[v(t1)+v(t2)]
Bvaverage=r(t2)r(t1)t2t1
Cv(t)=v(0)+at
Dr(t)=r(0)+v(0)t+12at2
• Question 3 - Select One

## If (12−t1)+(22−t2)++(n2−tn)+=n(n2−1)3 , then tn is equal to n2 b. 2n c. n2−2n d. none of these

An/2
Bn - 1
Cn + 1
Dn

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