Question

A particle starts with an initial velocity and passes suc-
cessively over the two halves of a given distance with
accelerations a, and a, respectively. Show that the fi-
nal velocity is the same as if the whole distance is cov-
ered with a uniform acceleration (a1+a2)/2​

Answer 1

Answer:

The distance is same in both the cases

Let it be s

If the initial velocity is u and the velocity is v' at the end of the first half then

using the third equation of the motion

$v'^2=u^2+2a_1s$  ........... (1)

v' will be the initial velocity for the second half, let the final velocity be v

Again

$v^2=v'^2+2a_2s$  ............(2)

Adding equation (1) and (2)

$v'^2+v^2=u^2+v'^2+2s(a_1+a_2)$

$\implies v^2=u^2+2(\frac{a_1+a_2}{2})\times 2s$

$\implies v^2=u^2+2A(2s)$

where, $A=\frac{a_1+a_2}{2}$

Therefore, the final velocity is the same as if the whole distance is covered with a uniform acceleration of $\frac{a_1+a_2}{2}$

Hope this answer is helpful.

Answer 2

Answer:

uniform acceleration is (a1+a2)/2