A point moves with uniform acceleration and v1,v2 and v3 denote the av

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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}

and

t_{3}

. Which of the following relations is correct?

Options:

A . (v1−v2):(v2−v3)=(t1−t2):(t2+t3)

B . (v1−v2):(v2−v3)=(t1+t2):(t2+t3)

C . (v1−v2):(v2−v3)=(t1−t2):(t1−t3)

D . (v1−v2):(v2−v3)=(t1−t2):(t2−t3)

Answer: Option B
:
B
Let

u_{1}, u_{2}, u_{3}

and

u_{4}

be velocities at time

t = 0, t_{1}, (t_{1} + t_{2})

and

(t_{1} + t_{2} + t_{3})

respectively and let theacceleration be

a

then

v_{1} = \frac{u_{1} + u_{2}}{2}, v_{2} = \frac{u_{2} + u_{3}}{2}

and

v_{3} = \frac{u_{3} + u_{4}}{2}

Also

u_{2} = u_{1} + a t_{1}, u_{3} = u_{1} + a (t_{1} + t_{2})

and

u_{4} = u_{1} + a (t_{1} + t_{2} + t_{3})

By solving, we get

\frac{v_{1} - v_{2}}{v_{2} - v_{3}} = \frac{t_{1} + t_{2}}{t_{2} + t_{3}}

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