Question

7.
A point moves with uniform acceleration
and v1,v2 and v3, denote the average
velocities in the three successive intervals
of time t1,t2 and t3 . Which of the following
relations is correct
(b) (v1-v2):(v2-v3)=(t1+t2):(t2+t3)
Solve it to get the answer... ​

Answer 1

Answer: The correct answer is $\frac{v_1 - v_2}{v_2 - v_3}$ = $\frac{t_1 + t_2}{t_2 + t_3}$

Explanation:

Given information in the question,

A point moves with uniform acceleration  and $v_1$ , $v_2$ and $v_3$ denote the average  velocities in the three successive intervals  of time $t_1$ , $t_2$ & $t_3$ respectively.

Let u be the initial velocity of the point.

∴ $v_1$ = u + a$t_1$

∴ $v_2$ = 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 + $\frac{1}{2}$ a$t_1$

$v_2$  = $\frac{v_1 + v_2}{2}$ = u + a$t_1$ + $\frac{1}{2}$ a$t_2$

$v_3$ = $\frac{v_2 + v_3}{2}$ = u + a$t_1$ + a$t_2$ +  $\frac{1}{2}$ a$t_3$

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

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

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

Answer 2

Answer:

Answer: The correct answer is =

Explanation:

Given information in the question,

A point moves with uniform acceleration  and , and denote the average  velocities in the three successive intervals  of time , & respectively.

Let u be the initial velocity of the point.

∴ = u + a

∴ = u + a()

∴ = u + a()

Now, we know, Average velocity = X (final velocity + initial velocty)

=

= = = u + a

 = = u + a + a

= = u + a + a +   a

∴ () = - a()  &

() =  - a()

∴   =

Read more on Brainly.in - https://brainly.in/question/11568816#readmore