Question

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 1

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 .