average velocity of a particle is 20m/s for time t . what should be th

1.	average velocity of a particle is 20m/s for time t . what should be the velocity of the particle for the next 2t seconds so that average speed is 10m/s
Answer» Given - Average velocity = 20 m/s for time t . TOTAL time = t + 2t seconds => 3t seconds Average speed = 10 m/s To find - => Velocity for next 2t seconds so that average speed is 10 m/s . Concepts/Formulae Used - » $\Large{Average\ Speed=\frac{Total\ Distance}{Total\ Time}}$ » $Velocity= \frac{Displacement}{Time}$ Note - => We have assumed distance and displacement to be the same here since it is rectilinear motion in a straight line. => So, we can interchangeably refer to the $\frac{d}{t}$ ratio as speed or velocity . LET's Solve - » Values that we already have - => We already know that the total time is 3t seconds. => We also know that the Average speed is 10 m/s . » For total distance - => Total distance = (distance COVERED in time t) + (distance covered in time 2t) . For distance in time t - => Average velocity = 20 m/s => Time = t seconds => $20 = \frac{Distance}{t}$ => Distance = 20t metres For distance in time 2t - => Let velocity for this be V m/s . => Time = 2t seconds => $v =\frac{Distance}{2t}$ => *Distance = 2t v metres Total distance = 20t + 2tv => 2t(10+v) metres » Finding the value of 'v' - Total time = 3t seconds Total distance = 2t(10 + v) metres Average speed = 10 m/s $\Large{Average\ Speed=\frac{Total\ Distance}{Total\ Time}}$ => $10 = \frac{2t(10+v)}{3t}$ => $10 = \frac{2(10+v)}{3}$ (t is cancelled) => $30 = 2(10+v)$ => 30 = 20 + 2v => 30-20 = 2v => 10 = 2v => 2v = 10 => v = 10/2 => v = 5 m/s** Answer - => The velocity of the PARTICLE for the next 2t seconds should be 5 m/s .

average velocity of a particle is 20m/s for time t . what should be the velocity of the particle for the next 2t seconds so that average speed is 10m/s

Answer» Given -

Average velocity = 20 m/s for time t .

TOTAL time = t + 2t seconds => 3t seconds

Average speed = 10 m/s

To find -

=> Velocity for next 2t seconds so that average speed is 10 m/s .

Concepts/Formulae Used -

» $\Large{Average\ Speed=\frac{Total\ Distance}{Total\ Time}}$

» $Velocity= \frac{Displacement}{Time}$

Note -

=> We have assumed distance and displacement to be the same here since it is rectilinear motion in a straight line.

=> So, we can interchangeably refer to the $\frac{d}{t}$ ratio as speed or velocity .

LET's Solve -

» Values that we already have -

=> We already know that the total time is 3t seconds.

=> We also know that the Average speed is 10 m/s .

» For total distance -

=> Total distance = (distance COVERED in time t) + (distance covered in time 2t) .

For distance in time t -

=> Average velocity = 20 m/s

=> Time = t seconds

=> $20 = \frac{Distance}{t}$

=> Distance = 20t metres

For distance in time 2t -

=> Let velocity for this be V m/s .

=> Time = 2t seconds

=> $v =\frac{Distance}{2t}$

=> Distance = 2t * v metres

Total distance = 20t + 2tv

=> 2t(10+v) metres

» Finding the value of 'v' -

Total time = 3t seconds

Total distance = 2t(10 + v) metres

Average speed = 10 m/s

$\Large{Average\ Speed=\frac{Total\ Distance}{Total\ Time}}$

=> $10 = \frac{2t(10+v)}{3t}$

=> $10 = \frac{2(10+v)}{3}$ (t is cancelled)

=> $30 = 2(10+v)$

=> 30 = 20 + 2v

=> 30-20 = 2v

=> 10 = 2v

=> 2v = 10

=> v = 10/2

=> v = 5 m/s