homework and exercises - Calculate acceleration and time given initial speed, final speed, and travelling distance?

A motorcycle is known to accelerate from rest to 190km/h in 402m.

Considering the rate of acceleration is constant, how should I go about calculating the acceleration rate and the time it took the bike to complete the distance?

Answer

For constant acceleration you have two equations that you need to solve for time $t$ and acceleration $a$

$$ x = \frac{1}{2} a t^2 $$ $$ v = a t $$

It is up to you from here.

$$ \left(402\, {\rm m}\right) = \frac{1}{2} \, a \,t^2 $$ $$ \left( 190 {\rm \frac{km}{hr}}\right) \left( \frac{1000 {\rm \frac{m}{km}}}{3600 {\rm \frac{sec}{hr}}} \right) = \left(52.777 {\rm \frac{m}{sec}} \right)\, a \,t $$