Distance traveled by a body is given by $2 S = (10 t + 5 t^{2}) m$ and $t$ is in seconds. The acceleration of the body is :

2.5 m s^{- 2}

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5 m s^{- 2}

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10 m s^{- 2}

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15 m s^{- 2}

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Solution

The correct option is C $5 m s^{- 2}$
$2 S = 10 t + 5 t^{2}$
$S = \frac{10 t + 5 t^{2}}{2}$
$\to a = \frac{d^{2} S}{d t^{2}} = \frac{d^{2}}{d t^{2}} (\frac{10 t + 5 t^{2}}{2}) = \frac{d}{d t} (\frac{10 + 10 t}{2})$ $= \frac{10}{2} = 5 m / s^{2}$

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Distance traveled by a body is given by 2S=(10t+5t2)m and t is in seconds. The acceleration of the body is :

The correct option is C 5ms−22S=10t+5t2S=10t+5t22→a=d2Sdt2=d2dt2(10t+5t22)=ddt(10+10t2)=102=5m/s2

Distance traveled by a body is given by $2 S = (10 t + 5 t^{2}) m$ and $t$ is in seconds. The acceleration of the body is :

The correct option is C $5 m s^{- 2}$
$2 S = 10 t + 5 t^{2}$
$S = \frac{10 t + 5 t^{2}}{2}$
$\to a = \frac{d^{2} S}{d t^{2}} = \frac{d^{2}}{d t^{2}} (\frac{10 t + 5 t^{2}}{2}) = \frac{d}{d t} (\frac{10 + 10 t}{2})$ $= \frac{10}{2} = 5 m / s^{2}$