Question

A body starts from rest with a uniform acceleration of $2\, m\, s^{-2}$ for 10 s, it moves with constant speed for 30 s then declerates by $4\, m\, s^{-2}$ to zero. the distance covered by the body is _____m

Answer 1

$u = 0,\, a = 2\, m\, s^{-2},\, t = 10\, s$
$\therefore \quad s_{1} = ut + \frac{1}{2}at^{2} = 0 +\frac{1}{2} \times2\times100 = 100\,m$
Velocity after $10 \,s,$
$\upsilon = u + at = 0 + 2 × 10 = 20 m\, s^{-1}$
$\therefore \quad s_{2} = \upsilon \times 30 = 20 \times 30 = 600\, m $
Final velocity $= 0,\, a = -4 \,m\, s^{-2}$
$\therefore \quad 0 = \upsilon^{2} + 2as_{3}$
$0 = \left(20\right)^{2} - 2 \times 4 \times s_{3}$
$\therefore \quad s_{3} = \frac{400}{8} = 50 \,m$
$\therefore \quad s = s_{1} + s_{2} + s_{3} = 100 + 600 + 50 = 750\, m$