A scooter accelerates from rest for timet1 at constant rate -1 and then retards at a constant rate -2 for timet2 and comes to rest- The correct value oft1-t2 will be-

Step 1. Given data :Time = t_1 and t_2 Constant rate = α 1 and α 2Step 2. Find V_∘for the first interval :From given information:α_1 = v_0/t_1v_0 = α_1t_1… ..(1 ...

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Standard XII

Mathematics

Integration by Partial Fractions

A scooter acc...

Question

A scooter accelerates from rest for time $t_{1}$ at constant rate $α_{1}$ and then retards at a constant rate $α_{2}$ for time $t_{2}$ and comes to rest. The correct value of $t_{1} / t_{2}$ will be:

$(α_{1} + α_{2}) / α_{2}$

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$α_{2} / α_{1}$

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$(α_{1} + α_{2}) / α_{1}$

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$α_{1} / α_{2}$

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Solution

The correct option is B
$α_{2} / α_{1}$

Step 1. Given data :
$T i m e = t_{1} a n d t_{2}$
$C o n s \tan t r a t e = α 1 a n d α 2$
Step 2. Find $V_{\circ}$ for the first interval :
From given information:
$α_{1} = v_{0} / t_{1}$
$v_{0} = α_{1} t_{1} \dots . . (1)$
Step 2. Find $V_{\circ}$ for the second interval :
$α_{2} = v_{0} / t_{2}$
$v_{0} = α_{2} t_{2} \dots . . (2)$
Step 3. Find the correct value of t₁/t₂:
From $(1)$ & $(2)$
$α_{1} t_{1} = α_{2} t_{2}$
$t_{1} / t_{2} = α_{2} / α_{1}$
Hence ,(B) option is correct.

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A scooter accelerates from rest for timet1 at constant rate α1 and then retards at a constant rate α2 for timet2 and comes to rest. The correct value oft1/t2 will be:

A scooter accelerates from rest for time $t_{1}$ at constant rate $α_{1}$ and then retards at a constant rate $α_{2}$ for time $t_{2}$ and comes to rest. The correct value of $t_{1} / t_{2}$ will be: