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Acceleration

Ifa body is m...

Question

Ifa body is moving with a uniform acceleration $a_{1}$ for time $t_{1}$ and with uniform acceleration $a_{2}$ for time $t_{2}$ then its average acceleration is

\frac{a_{1} + a_{2}}{t_{1} t_{2}}

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\frac{a_{1} + a_{2}}{t_{1} + t_{2}}

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\frac{a_{1} t_{1} + a_{2} t_{2}}{t_{1} + t_{2}}

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\frac{a_{1} t_{1} + a_{2} t_{2}}{a_{1} + a_{2}}

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Solution

The correct option is C $\frac{a_{1} t_{1} + a_{2} t_{2}}{t_{1} + t_{2}}$
Relation between initial velocity and final velocity is
$v_{f i n a l} = v_{i n i t i a l} + a t$
For the duration of $t_{1}$ initial velocity is 0 and acceleration is $a_{1}$ so final velocity is
$v_{1} = 0 + a_{1} t_{1}$

For the duration $t_{2}$ initial velocity is $v_{1}$ and acceleration is $a_{2}$ so final velocity is
$⟹ v_{2} = v_{1} + a_{2} t_{2}$
$⟹ v_{2} = a_{2} t_{2} + a_{1} t_{1}$

average acceleration is
$a_{a v e r a g e} = \frac{v_{f i n a l} - v_{i n i t i a l}}{t_{t o t a l}}$

$a_{a v e r a g e} = \frac{v_{2} - v_{0}}{t_{1} {+ t}_{2}}$

$a_{a v e r a g e} = \frac{a_{2} t_{2} + a_{1} t_{1}}{t_{1} {+ t}_{2}}$

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Ifa body is moving with a uniform acceleration a1 for time t1 and with uniform acceleration a2 for time t2 then its average acceleration is

Ifa body is moving with a uniform acceleration $a_{1}$ for time $t_{1}$ and with uniform acceleration $a_{2}$ for time $t_{2}$ then its average acceleration is