How long does it take a motor cyclist to come to rest?which travels at 12m/s decelerates at 3m/s^2

Divide the speed change (12 m/s in this case) by the acceleration (or deceleration) rate

4m/s

To calculate how long it takes for a motorcyclist to come to rest, we can use the equation of motion:

vf = vi + at

Where:
vf = final velocity (which is zero as the motorcyclist comes to rest)
vi = initial velocity (12 m/s)
a = acceleration (deceleration, which is -3 m/s^2 because it is in the opposite direction)
t = time

Rearranging the equation, we get:

t = (vf - vi) / a

Plugging in the values we know:

t = (0 - 12) / -3

Simplifying, we get:

t = 12 / 3

t = 4 seconds

Therefore, it will take the motorcyclist 4 seconds to come to rest.