The light turns green, and a bicyclist starts forward with an acceleration of 1.4 m/s^2?

initial vel., u=0 (as cycle starts frm rest)

accleration, a=1.4m/s^2

final vel., v=7.7m/s

now, v=u + at

or v=at (as u is 0)

or t=v/a

or t=7.7/1.4

or t=5.5s

Dist. travld = 1/2at^2=1/2.1.4*5.5^2=21.175m

First of all, Kara, lets figure how long it will take her to reach a sped of 7.7 m/s. well. you're probably familiar with the formula:

V = aT so we substitute 7 m/s = 1.4m/s2 (T) or T = 7 m/s / 1.4m/s2

which comes out to be 5.5 seconds. Now you probably also know that X = vt

or distance = velocity x time. Well, the velocity isn't given; she's accelerating all the time. But Kara, the average velocity is equal to one half the final velocity. If she starts from zero and ends at 7.7 m/s. then half of the time she's going slower than 3.85 m/s and half the time she's going faster than 3.85 m/s. If her average speed is 3.85 m/s and you multiply that times 5.5 seconds you get a distance of 21.175 meters. I suppose you should know the formula for finding the average velocity which is:

V (ave) = V (final) - V (initial) divided by 2 .....anyway, the answer is 21.175 meters. I could have just given you formulas to plug the numbers into, but I think it's really important to really understand what's going on. I hope I helped!

You can use this kinematic equation:

V^2 = Vo^2 + 2ad

Substituting known values:

(7.7)^2 = (0)^2 + 2(1.4)d

Solve for d

d = 21.175 m