0

Guest

Courses New

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)

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)

Grade:9

2 Answers

Vikas TU
14149 Points
6 years ago
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. 4th year
Thapar University)
ankit singh
askIITians Faculty 614 Points
3 years ago
 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}
 
 

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More