The motion of a particle along a straight line is described by equation x=8+12t-t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

Question

The motion of a particle along a straight line is described by equation x=8+12t-t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is (A) 24ms- 2 (B) Zero (C) 6 m s- 2 (D) 12 m s- 2

Tardigrade Admin · Accepted Answer

Given: x = 8 + 12 12t - t3 textVelocity, textv = ( d x/ d â¡ t) = 1 2 - 3 t2 When v = 0, 12 - 3t2 = 0 or t = 2 s a = ( d v â¡/ d â¡ t) = - 6 t a|t = 2 s = - 12 m s-2 Retardation = 12 m s-2

Q. The motion of a particle along a straight line is described by equation $x = 8 + 12 t - t^{3}$ where $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero is

$24 m s^{- 2}$

Zero

$6 m s^{- 2}$

$12 m s^{- 2}$

Given : $x$ = 8 + 12 12t - t³
$Velocity, v = \frac{d x}{d t} = 12 - 3 t^{2}$
When v = 0, 12 - 3t²= 0 or t = 2 s
$a = \frac{d v}{d t} = - 6 t$
a|_{t = 2 s} = - 12 m s^-2
Retardation = 12 m s^-2

Q. The motion of a particle along a straight line is described by equation x=8+12t−t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

24ms−2

Zero

6ms−2

12ms−2

Given : x = 8 + 12 12t - t3 Velocity,v=d⁡tdx​=12−3t2 When v = 0, 12 - 3t2 = 0 or t = 2 s a=d⁡tdv⁡​=−6t a|t = 2 s = - 12 m s-2 Retardation = 12 m s-2

Q. The motion of a particle along a straight line is described by equation $x = 8 + 12 t - t^{3}$ where $x$ is in metre and $t$ in second. The retardation of the particle when its velocity becomes zero is

$24 m s^{- 2}$

$6 m s^{- 2}$

$12 m s^{- 2}$

Given : $x$ = 8 + 12 12t - t³
$Velocity, v = \frac{d x}{d t} = 12 - 3 t^{2}$
When v = 0, 12 - 3t²= 0 or t = 2 s
$a = \frac{d v}{d t} = - 6 t$
a|_{t = 2 s} = - 12 m s^-2
Retardation = 12 m s^-2