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Standard XII

Physics

Finding Average Velocity

Velocity of p...

Question

Velocity of particle varies with time as $v = t^{2} - 5 t + 6$ . The motion of the particle will be :

accelerating for

t ϵ (2, 2.5)

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retarding for

t ϵ (2, 2.5)

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accelerating for

t ϵ (2.5, 3)

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retarding for

t ϵ (2.5, 3)

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Solution

The correct options are
B retarding for $t ϵ (2.5, 3)$
C accelerating for $t ϵ (2, 2.5)$
Differentiating and solving for various values of $t$ ,
at $t = 2 s \Rightarrow v = 0, a = - 1$
at $t = 2.5 s \Rightarrow v = - 0.25, a = 0$
at $t = 3 s \Rightarrow v = 0, a = 1$
Thus,
For $t ϵ (2, 2.5)$ speed $↑$ in negative direction so motion is accelerated
For $t ϵ (2.5, 3)$ speed $↓$ in negative direction so motion is decelerating.

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Velocity of particle varies with time as v=t2−5t+6. The motion of the particle will be :

Velocity of particle varies with time as $v = t^{2} - 5 t + 6$ . The motion of the particle will be :