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A car starts from rest and moves on straight line with constant acceleration $a_{0}$ . After time $t_{0}$ , brakes is applied which cause of deceleration of magnitude as initial acceleration. The distance travelled by car is

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a

$\frac{1}{2} a_{0} t_{0}^{2}$

b

$2 a_{0} t_{0}^{2}$

c

$a_{0} t_{0}^{2}$

d

$\frac{2}{3} a_{0} t_{0}^{2}$

answer is C.

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Detailed Solution

$s_{1} = \frac{1}{2} a_{0} t_{0}^{2} v_{0} = a_{0} t_{0} v^{2} = u^{2} - 2 a s 0^{2} = v_{0}^{2} - 2 a_{0} s_{2} s_{2} = \frac{v_{0}^{2}}{2 a_{0}} = \frac{{(a_{0} t_{0})}^{2}}{2 a_{0}} = \frac{1}{2} a_{0} t_{0}^{2}$

$∴$ Total distance travelled,

$s = s_{1} + s_{2} = a_{0} t_{0}^{2}$

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