First slide

Instantaneous acceleration

Question

A car starting from rest, travels with uniform acceleration x and then comes to rest with uniform retardation y. If the total time of travel is t sec, the maximum velocity of the car is

Moderate

A

$\frac{xyt}{(x + y)}$
B

$\frac{xy}{t (x + y)}$
C

$\frac{yt}{x (x + y)}$
D

$\frac{xt}{y (x + y)}$

Solution

In accelerated motion,
$\begin{array}{l} V = u + {xt}_{1} = 0 + {xt}_{1} \\ â´ â V = {xt}_{1} . . . . (1) \end{array}$
When the car stops (after retardation)
$0 = v â y (t â t_{1})$
where t =total time,
t₁ = time of acceleration, and
t₂ = time of retardation
$â´ v = y (t â t_{1}) . . . . (2)$
From eqs. (1) and (2)
${xt}_{1} = y (t â t_{1}) = yt â {yt}_{1}$
Solving, we get $t_{1} = yt / (x + y)$
From eq,(1), $v = \frac{xyt}{(x + y)}$

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