Given,
A body accelerates from rest and travels S1 in t seconds.
After that it travels uniformly with acquired velocity for next t second and covers S2.
To Find :
Relation between S1 and S2.
During first t seconds, body is moving with constant acceleration means velocity will vary with time.
Let acceleration of body be a.
Initial velocity of body is zero.
Let's apply second equation of kinematics.
➙ S1 = ut + 1/2 at2
➙ S1 = (0 × t) + 1/2 at2
➙ S1 = 1/2 at2 ..... (i)
Final velocity of body after time t :
➝ v = u + at
➝ v = 0 + at
➝ v = at
Final velocity of first case will be initial velocity of second case. In this case body is moving with a constant velocity
⇒ velocity = distance / time
⇒ at = S2 / t
⇒ S2 = at2 ..... (ii)
Taking ratio of (i) & (ii), we get
⇒ S1 / S2 = \(\frac {1}{2}\,\frac{at^2}{at^2}\)
⇒ S1 / S2 = 1/2
⇒ S2 = 2S1
