(A) Let the initial acceleration be $a_1$. Since the car starts from rest,$u = 0$. After $t_1 = 9 \ s$,the velocity becomes $v = a_1 t_1 = 9a_1$. Thus

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(A) Let the initial acceleration be $a_1$. Since the car starts from rest,$u = 0$. After $t_1 = 9 \ s$,the velocity becomes $v = a_1 t_1 = 9a_1$. Thus,$a_1 = v/9$.Next,the motorist maintains the speed $v$ for $t_2 = 50 \ s$.Finally,the motorist decelerates to rest. Let the deceleration be $a_2$. We are given $a_2 = 3a_1 = 3(v/9) = v/3$.Using the equation of motion $v_f = u_f - a_2 t_3$,where $v_f = 0$ (final rest),$u_f = v$ (initial speed for this phase),and $t_3$ is the time taken to stop:$0 = v - (v/3) t_3$$v = (v/3) t_3$$t_3 = 3 \ s$.

Class 11 Physics Motion in a Straight Line Uniformly Accelerated Motion

Medium

$A$ motorist starting a car from rest accelerates uniformly to a speed of $v \ m/s$ in $9 \ s$. He maintains this speed for another $50 \ s$ and then applies the brakes and decelerates uniformly to rest. His deceleration is numerically equal to three times his previous acceleration. Then the time during which the deceleration takes place is .......... $s$ :-

A
$3$
B
$9$
C
$27$
D
$6$

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Class 11

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Motion in a Straight Line

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Uniformly Accelerated Motion

$A$ particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2 = 1 + t^2$. Its acceleration at any time $t$ is $x^{-n}$ where $n = . . . . .$

DifficultJEE MAIN 2024

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$A$ car accelerates from rest at a constant rate $\alpha$ for some time,after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed is $t$,then the maximum velocity acquired by the car is

DifficultAIPMT 1994

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An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement $(s)-$ velocity $(v)$ graph of this object is

MediumAP EAMCET 2021

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$A$ body $A$ starts from rest with an acceleration $a_1$. After $2$ seconds,another body $B$ starts from rest with an acceleration $a_2$. If they travel equal distances in the $5$th second after the start of $A$,then the ratio $a_1:a_2$ is equal to

MediumAIIMS 2001

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$A$ small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of $10 \, m$ in $t \, s$,the distance travelled by the toy in the next $t \, s$ will be ......... $m$.

MediumJEE MAIN 2022

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$A$ particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2 = 1 + t^2$. Its acceleration at any time $t$ is $x^{-n}$ where $n = . . . . .$

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