A bus accelerates from the rest for time t1 at a constant rate - then retards at a constant rate - for time t2 and comes to rest- Then t1-t2

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Standard XII

Physics

Deducing Mathematically

A bus acceler...

Question

A bus accelerates from the rest for time $t_{1}$ at a constant rate $α$ then retards at a constant rate $β$ for time $t_{2}$ and comes to rest, Then $t_{1} / t_{2}$

\frac{α}{β + α}

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\frac{β + α}{2}

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\frac{β + α}{α}

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\frac{β}{α}

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Solution

The correct option is D $\frac{β}{α}$
Let maximum velocity achieved $= v_{m a x}$
$v_{m a x} = 0 + α t_{1} = α t_{1}$
Also $0 = v_{m a x} - β t_{2} \Rightarrow v_{m a x} = β t_{2}$
$∴ α t_{1} = β t_{2} \Rightarrow \frac{t_{1}}{t_{2}} = \frac{β}{α}$

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A bus accelerates from the rest for time t1 at a constant rate α then retards at a constant rate β for time t2 and comes to rest, Then t1/t2

The correct option is D βαLet maximum velocity achieved =vmaxvmax=0+αt1=αt1Also 0=vmax−βt2⇒vmax=βt2∴αt1=βt2⇒t1t2=βα

A bus accelerates from the rest for time $t_{1}$ at a constant rate $α$ then retards at a constant rate $β$ for time $t_{2}$ and comes to rest, Then $t_{1} / t_{2}$

The correct option is D $\frac{β}{α}$
Let maximum velocity achieved $= v_{m a x}$
$v_{m a x} = 0 + α t_{1} = α t_{1}$
Also $0 = v_{m a x} - β t_{2} \Rightarrow v_{m a x} = β t_{2}$
$∴ α t_{1} = β t_{2} \Rightarrow \frac{t_{1}}{t_{2}} = \frac{β}{α}$