Q: A block of mass 1 kg starts from rest on a straight road whose acceleration versus displacement graph is shown in the figure. Find the increase in kinetic energy if speed increases as it travels a distance 10 m.
(a) Non – zero
(b) 20 J
(c) 40 J
(d) 50 J
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Ans: (a) , (d)
Sol: $\displaystyle v^2 = u^2 + 2 a s $
$\displaystyle v^2 – u^2 = 2 a s $
$\displaystyle v^2 – u^2 = 2 \times area \; of \; a-s \; graph $
Multiplying by 1/2 ,
$\displaystyle \frac{1}{2}(v^2 – u^2 ) = \frac{1}{2} ( 2 \times area \; of \; a-s \; graph )$
$\displaystyle \Delta K.E = area \; of \; a-s \; graph $
$\displaystyle \Delta K.E = \frac{1}{2} \times 10 \times 10 $
= 50 J