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. What final velocity does the motorcycle attain?

√ (6ax)

Explanation:

Hi!

The question states that during a time t the motorcyle underwent a displacement x at constant acceleration a starting from rest, mathematically we can express it as:

x = (1/2) at^2

Then the we need to find the time t' for which the displacement is 3x

3x = (1/2) a (t') ^2

Solving for t':

t'=√ (6x/a)

Now, the velocity of the motorcycle as a function of time is:

v (t) = a*t

Evaluating at t=t'

v (t') = a*√ (6x/a) = √ (6*x*a)

Which is the final velocity

Have a nice day!