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  4. A particle moving in a straight line with uniform acceleration is observed to be a distance a from a fixed point initially. It is at distances b, c, d from the same point after n, 2 n, 3 n second. The acceleration of the particle is

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Q. A particle moving in a straight line with uniform acceleration is observed to be a distance $a$ from a fixed point initially. It is at distances $b, c, d$ from the same point after $n, 2\, n, 3\, n$ second. The acceleration of the particle is

Motion in a Straight Line

Solution:

As, $b-a=u n+\frac{1}{2} A n^{2}$
$\therefore 2 b-2 a=2 u n+A n^{2}$ ......(i)
image
Again, $C - a =u(2 n)+\frac{1}{2} A (2 n)^{2}$ .......(ii)
Subtracting, Eq. (i) in Eq. (ii), we get
$c-a-2 b+2 a =A n^{2} $
$A =\frac{c-2 b+a}{n^{2}}$