Question

A particle is travelling with uniform acceleration of magnitude 'a'. During successive time intervals of
Δ
t
1
,
Δ
t
2
and
Δ
t
3
, its average velocities are
v
1
,
v
2
and
v
3
respectively. Then,

Answer 1

The value of v1 - v2 / v2 - v3 =  t1 + t2 / t2 + t3

Explanation:

Correct statement:

A particle moving with uniform acceleration has average velocities v1 , v2  and v3  over the successive intervals of time t1 , t2  and t3  respectively. The value of  (v  1 −v  2 )  /   (v  2 −v  3  ) will be.

Solution:

Let say the particles move with time intervals t1, t2, and t3.

• Velocity at B = u + at1
• Velocity at C = u + a ( t1 + t2)
• Velocity at D = u + a ( t1 + t2 + t3 )
• Average velocity = [ Initial velocity + Final velocity ] / 2

Average velocity = [ u + u at1 ] / 2

Average velocity = [ u + at1 / 2 ]

V2 = u + at1 + at2  / 2

V3 = u + at1 at2 + at3 / 2

Now solving the equations we get.

v1 - v2 / v2 - v3 = t1 + t2 / t2 + t3

Thus the value of v1 - v2 / v2 - v3 =  t1 + t2 / t2 + t3