Question

a body covers with uniform acceleration in a straight line, distance A and B in successive intervals of time t1 and t2. What is the acceleration of the body?​

Answer 1

Answer:

There's small correction. We have to prove 1/T1 - 1/T2 + 1/T3 = 3 / (T1 + T2 + T3).

◆ Proof -

Let v0, v1, v2 & v3 be velocities at time 0, after T1, after T1+T2 & after T1+T2+T3 respectively.

Now, average velocities in respective timeframes can be given by -

During T1, s/T1 = (v0+v1)/2 ...(1)

During T2, s/T2 = (v1+v2)/2 ...(2)

During T1, s/T3 = (v2+v3)/2 ...(3)

Average velocity during this time interval -

(s + s + s) / (T1 + T2 + T3) = (v0 + v3) / 2

3s / (T1 + T2 + T3) = (v0 + v3) / 2 ...(4)

Now, eqn.(1) - eqn.(2) + eqn.(3)

s/T1 - s/T2 + s/T3 = (v0+v1)/2 - (v1+v2)/2 + (v2+v3)/2

s (1/T1 - 1/T2 + 1/T3) = (vo + v1 - v1 - v2 + v2 + v3) / 2

s (1/T1 - 1/T2 + 1/T3) = (v0 + v3) / 2

From eqn.(4),

s (1/T1 - 1/T2 + 1/T3) = 3s / (T1 + T2 + T3)

1/T1 - 1/T2 + 1/T3 = 3 / (T1 + T2 + T3)

Explanation: