Question

-14. A particle moves along a straight line such that its displacement (s) at any time
(1) is given by S = t3-6t2+3t+4. The velocity of the particle when its acceleration
zero is
1) 3 units
2) -8 units
3) 6units
4) -9 units
​

Answer 1

Answer:

i think that the answer for your question is 6 units

Answer 2

Given :

• A particle moves along a straight line such that its displacement at any time (t) is given by s = t³ - 6 t² + 3 t + 4

To find :

• Velocity of the particle when its acceleration is zero, v = ?

Knowledge required :

• The instantaneous velocity of body is given by the derivative of position of body (s), with respect to time (t) .

$\red{\bigstar}\boxed{\sf{v(t)=\dfrac{d\;(s)}{d\;(t)}}}$

• The instantaneous acceleration of body is given by the derivative of velocity of body (v), with respect to time (t) .

$\red{\bigstar}\boxed{\sf{a(t)=\dfrac{d\;(v)}{d\;(t)}}}$

Solution :

Using formula for instantaneous velocity

$\longrightarrow\sf{v(t)=\dfrac{d\;(s)}{d\;(t)}}$

putting value of (s) = t³ - 6 t² + 3 t + 4

$\longrightarrow\sf{v(t)=\dfrac{d\;(t^3-6t^2+3t+4)}{d\;(t)}}$

differentiating

$\longrightarrow\underline{\underline{\red{\sf{v(t)=3t^2-12t+3}}}}$

Using formula for instantaneous acceleration

$\longrightarrow\sf{a(t)=\dfrac{d\;(v)}{d\;(t)}}$

putting value of (v) = 3 t² - 12 t + 3

$\longrightarrow\sf{a(t)=\dfrac{d\;(3t^2-12t+3)}{d\;(t)}}$

differentiating

$\longrightarrow\underline{\underline{\red{\sf{a(t)=6t-12}}}}$

Calculating [ t ] when acceleration will be zero

$\longrightarrow\sf{a(t)=6t-12=0}$

$\longrightarrow\sf{6t=12}$

$\longrightarrow\underline{\underline{\red{\sf{t=2}}}}$

Calculating velocity of particle when its acceleration will be zero, i.e, at  [t = 2]

$\longrightarrow\sf{v(t)=3t^2-12t+3}$

$\longrightarrow\sf{v(2)=3\times(2)^2-12\times(2)+3}$

$\longrightarrow\sf{v(2)=12-24+3}$

$\longrightarrow\boxed{\underline{\underline{\large{\red{\sf{v(2)=-9\;units}}}}}}$

therefore,

• Velocity of particle at acceleration being zero will be -9 units .

Hence,

• OPTION (4) -9 units is Correct.