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Q.
A body covers 200 cm in the first 2 seconds and 220 cm in the next 4 seconds. The velocity of the body at the end of the $7^{th}$ second is
Motion in a Straight Line
Solution:
Let u and a be the initial velocity and uniform acceleration of the body.
Using $ S = ut + \frac{1}{2}at^{2}$
$\therefore \quad 200 = u\left(2\right) + \frac{1}{2}a\left(2\right)^{2}$
$100 = u + a\quad ...\left(i\right)$
Also $420 = 6u +\frac{1}{2}a\left(6\right)^{2}$
$70 = u + 3a \quad...\left(ii\right)$
Solving equations $\left(i\right)$ and $\left(ii\right)$, we get
$u = 115\, cm\, s^{-1}, a = - 15\, cm \,s^{-2}$
Using $\upsilon = u + at$
$\therefore \quad\upsilon = 115 + \left(-15\right)7 = 10 \,cm\, s^{-1}$
