Question

A particle is moving along a straight line given by the reactions s=2-3t+4t^3 where s is in cms and t in sec its average velocity during third sec is

Answer 1

AnswEr :

Given :

• The distance travelled by the particle is given as : 4t³ - 3t + 2

• Time taken (t) = 3 seconds

To finD :

Average Velocity of the particle

Explanation :

$\underline{\underline{\sf Average \ Velocity \colon}}$

• Total distance travelled by a particle in certain instance of time is termed as Average Velocity

• SI Unit is m/s

• Dimensional Formula is given as [MT^-1]

Mathematically,

$\large \rm \bar{v} = \dfrac{\Delta{s}}{\Delta{t}}$

Now,

$\longrightarrow \: \rm \bar{v} = \dfrac{s_2 - s_1}{t_2 - t_1} \\ \\ \longrightarrow \: \rm \bar{v} = \frac{ \{4( {3}^{3}) - 3(3) + 2 \} - \{ 0(3 {}^{3} )- 0(3) + 2 \} }{3 - 0} \\ \\ \longrightarrow \: \rm \bar{v} = \frac{(108 - 9 + 2) - 2}{3} \\ \\ \longrightarrow \: \rm \bar{v} = \cancel{\dfrac{99}{ 3}} \: 33 \\ \\ \longrightarrow \boxed{ \boxed{ \rm \bar{v} = 33 \: {ms}^{ - 1}}}$

Average Velocity of the particle in the first three seconds is 33 m/s