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