A cyclist is at rest at a traffic light. When the light turns green, he begins accelerating at 2.56 m/s2. How far does he go after the light turns green until he reaches a cruising speed of 10.88 m/s?

get t from

v = a t

then get d from
d = (1/2) a t^2

To find the distance the cyclist travels until they reach a cruising speed, we can make use of the equations of motion.

We are given:
Initial velocity (u) = 0 m/s (as the cyclist is at rest)
Acceleration (a) = 2.56 m/s^2
Cruising speed (v) = 10.88 m/s

We need to find the distance (s) covered during this period.

We can use the equation of motion:

v^2 = u^2 + 2as

Rearranging this equation to solve for distance (s):

s = (v^2 - u^2) / (2a)

Now plugging in the values:

s = (10.88^2 - 0^2) / (2 * 2.56)
s = (118.54) / 5.12
s = 23.15 meters

Therefore, the cyclist travels approximately 23.15 meters until they reach the cruising speed of 10.88 m/s.