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) 24 m s-2 (B) zero (C) 6 m s-2 (D) 12 m s-2

Tardigrade Admin · Accepted Answer

Given: x=8+12 t-t3 Velocity, v=(d x/d t)=12-3 t2 When v=0,12-3 t2=0 or t=2 s a=(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 $x = 8 + 12 t - t^{3}$ 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 : $x = 8 + 12 t - t^{3}$
Velocity, $v = \frac{d x}{d t} = 12 - 3 t^{2}$
When $v = 0, 12 - 3 t^{2} = 0$
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+12t−t3 Velocity, v=dtdx​=12−3t2 When v=0,12−3t2=0 or t=2s a=dtdv​=−6t a∣t=2s​=−12ms−2 Retardation =12ms−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 : $x = 8 + 12 t - t^{3}$
Velocity, $v = \frac{d x}{d t} = 12 - 3 t^{2}$
When $v = 0, 12 - 3 t^{2} = 0$
or $t = 2 s$
$a = \frac{d v}{d t} = - 6 t$
$a ∣_{t = 2 s} = - 12 m s^{- 2}$
Retardation $= 12 m s^{- 2}$