If a particle is accelerated for time T with acceleration ao and for time T2 with acceleration 2ao then average acceleration

The correct option is D 4a_o3 Suppose initial velocity = u #160;after time T velocity #160; = u + a_0T after T +T/2 velocity #160; = (u ...

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Standard VIII

Physics

Acceleration

If a particle...

Question

If a particle is accelerated for time $T$ with acceleration $a_{o}$ and for time $\frac{T}{2}$ with acceleration $2 a_{o}$ then average acceleration

a_{o}

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\frac{2 a_{o}}{3}

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\frac{3 a_{o}}{2}

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\frac{4 a_{o}}{3}

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Solution

The correct option is D $\frac{4 a_{o}}{3}$
Suppose initial velocity = u
after time T velocity $= u + a_{0} T$
after $T + \frac{T}{2}$ velocity $= (u + a_{0} T) + 2 a_{0} \frac{T}{2}$
$= u + 2 a_{0} T$
$\Rightarrow$ change in velocity $= u + 2 a_{0} T - u = 2 a_{0} T - U = 2 a_{0} T$
$\Rightarrow$ average acceleration a = $\frac{Δ v}{Δ t} = \frac{2 a_{0} T}{T + \frac{T}{2}}$
$\Rightarrow a = \frac{4 a_{0} T}{3 T} = \frac{4 a_{0}}{3}$
option D is correct

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If a particle is accelerated for time T with acceleration ao and for time T2 with acceleration 2ao then average acceleration

The correct option is D 4ao3Suppose initial velocity = u after time T velocity =u+a0Tafter T+T2 velocity =(u+a0T)+2a0T2=u+2a0T⇒ change in velocity =u+2a0T−u=2a0T−U=2a0T⇒ average acceleration a = ΔvΔt=2a0TT+T2⇒a=4a0T3T=4a03 option D is correct

If a particle is accelerated for time $T$ with acceleration $a_{o}$ and for time $\frac{T}{2}$ with acceleration $2 a_{o}$ then average acceleration