Question

Car accelerates uniformly from rest to reach velocity (v) and covers distance (d) then the velocity of the car when it covers distance equal 2d ?

car accelerates uniformly from rest to reach velocity (v) and covers distance (d) then the velocity of the car when it covers distance equal 2d

Answer 1

`v_"new" = 1.414*v`

Explanation:

I assume it continues the same uniform acceleration when going from d to 2d.

The acceleration can be determined from the story up to distance d. Using the following formula of the basic set of 4 kinematic formulas `darr`

`v^2 = u^2 + 2*a*s`

`v^2 = 0^2 + 2*a*s`

`a = v^2/(2*d)`

Now we will repeat use of that formula for the duration, from start to distance 2d, use that expression for the acceleration.

`v_"new"^2 = 0^2 + cancel(2)*v^2/(cancel(2)*cancel(d))*2*cancel(d)`

`v_"new"^2 = 2*v^2`

`v_"new" = sqrt(2*v^2) = 1.414*v`

I hope this helps,
Steve