A body starting from rest, accelerates at a constant rate a ms -2 for some time after which it decelerates at a constant rate b ms -2 to come to rest finally. If the total time elapsed is t sec, the maximum velocity attained by the body is given by

Question

A body starting from rest, accelerates at a constant rate a ms -2 for some time after which it decelerates at a constant rate b ms -2 to come to rest finally. If the total time elapsed is t sec, the maximum velocity attained by the body is given by (A) (a b/a+b) t ms -1 (B) (a b/a-b) t ms -1 (C)  (2ab/a+b)t ms-1  (D)  (2ab/a-b)t ms-1

Tardigrade Admin · Accepted Answer

When the body accelerates initial velocity

u = 0

acceleration

= a

and time

= t_{1}

then final velocity

v = 0 + a t_{1} \dots

(i)
Now, as the body decelerates initial velocity,

= v

deceleration

= - b

and time

= (t - t_{1})

[t =

total time elapsed

]

final velocity here

v_{2} = 0

Again

0 = v - b (t - t_{1}) \dots

(ii)
From Eqs. (i) and (ii), we get

a t_{1} = b (t - t_{1})

or

(a + b) t_{1} = b t

\Rightarrow t_{1} = \frac{b t}{( a + b )}

Substituting the value of

t_{1}

in Eq. (i), we get

v = \frac{ab t}{( a + b )} m s^{- 1}

Q. A body starting from rest, accelerates at a constant rate $a m s^{- 2}$ for some time after which it decelerates at a constant rate $b m s^{- 2}$ to come to rest finally. If the total time elapsed is $t sec$ , the maximum velocity attained by the body is given by

$\frac{ab}{a + b} t m s^{- 1}$

$\frac{ab}{a - b} t m s^{- 1}$

$\frac{2 ab}{a + b} t m s^{- 1}$

$\frac{2 ab}{a - b} t m s^{- 1}$

Q. A body starting from rest, accelerates at a constant rate ams−2 for some time after which it decelerates at a constant rate bms−2 to come to rest finally. If the total time elapsed is tsec, the maximum velocity attained by the body is given by

a+bab​tms−1

a−bab​tms−1

a+b2ab​tms−1

a−b2ab​tms−1

Q. A body starting from rest, accelerates at a constant rate $a m s^{- 2}$ for some time after which it decelerates at a constant rate $b m s^{- 2}$ to come to rest finally. If the total time elapsed is $t sec$ , the maximum velocity attained by the body is given by

$\frac{ab}{a + b} t m s^{- 1}$

$\frac{ab}{a - b} t m s^{- 1}$

$\frac{2 ab}{a + b} t m s^{- 1}$

$\frac{2 ab}{a - b} t m s^{- 1}$