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# Kinematics Question - Check Your Understanding

## Question

1. A motorcycle starts from rest and has a constant acceleration. In a time interval t, it undergoes a displacement x and attains a final velocity v. Then t is increased so that the displacement is

3x. In this same increased time interval, what final velocity does the motorcycle attain?

The book says the answer is 1.73 v, but my teacher gave a bunch of variables when he solved it.

Edited by Daemidra

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This question can be solved using one of the Equations of Motion, namely v^2 = u^2 + 2ax where
v is the final velocity, u is the initial velocity, a is the acceleration and x is the displacement.

Since the motorcycle starts from zero u =0 and can be discarded from the equation.
The equation is now v^2 = 2ax
If the displacement changes to 3x our equation becomes (new v)^2 = 2a3x
(new v)^2 = 6ax
but the velocity in the first case was given by v^2 =2ax: (new v)^2 = 3 v^2
Square root both sides new v = square root of 3 times v
Square root of 3 is 1.73

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Nicely done Daemidra.

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