Mechanics> a particle moves with constant accelerati...

a particle moves with constant acceleration. if v1, v2 and v3 are three average velocities in three successive intervals t1, t2 and t3 of time, then prove that (v1-v2) /(v2-v3) = (t1+t2)/(t2+t3)

Ramesh Chandra , 8 Years ago

Grade 9

2 Answers

Vikas TU

Dear Student,

Assume the particles moves the separation AB, BC and CD in time t1,t2 and t3 individually.

Speed at B = u+at1

Speed at C = u+a(t1+t2)

Speed at D = u + a( t1+t2+t3)

Normal speed (v1)=( starting +final)/2

= (u + u + at1)/2

= u+1/2 at1

V2 = u+at1+1/2at2

V3 = u+ at1+at2+1/2at3

There fore we get

(V1-V2)/(V2-V3) = (t1+t2)/(t2+t3)
Hence proved.

Cheers!!

Regards,

Vikas (B. Tech. 4^th year
Thapar University)

Last Activity: 8 Years ago

ankit singh

v_1 = u + at_1

∴ v_2 = u + a(t_1 + t_2)

∴ v_3 = u + a(t_1 + t_2 + t_3)

Now, we know, Average velocity = \frac{1}{2} X (final velocity + initial velocty)

= \frac{v+u}{2}

v_1 = \frac{u + v_1}{2} = \frac{u + u + at_1}{2} = u + \frac{1}{2} at_1

v_2 = \frac{v_1 + v_2}{2} = u + at_1 + \frac{1}{2} at_2

v_3 = \frac{v_2 + v_3}{2} = u + at_1 + at_2 + \frac{1}{2} at_3

∴ (v_1 - v_2) = - \frac{1}{2} a(t_1 + t_2) &

(v_2 - v_3) = - \frac{1}{2} a(t_2 + t_3)

∴ \frac{v_1 - v_2}{v_2 - v_3} = \frac{t_1 + t_2}{t_2 + t_3}

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Mechanics> a particle moves with constant accelerati...

a particle moves with constant acceleration. if v1, v2 and v3 are three average velocities in three successive intervals t1, t2 and t3 of time, then prove that (v1-v2) /(v2-v3) = (t1+t2)/(t2+t3)

Ramesh Chandra , 8 Years ago

Vikas TU

ankit singh

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