Answer:
I will answer in English.
Ok, we know that the acceleration is a = 18m/s^2, and we have that the initial velocity and position are both zero. (because it starts at rest)
then we have:
a(t) = 18m/s^2
for the velocity, we integrate over time (because the initial velocity is equal to zero we do not have any integration constant)
v(t) = (18m/s^2)*t
for the position we integrate again over time, and again, we do not have any integration constant
p(t) = (1/2)(18m/s^2)*t^2 = (9m/s^2)*t^2
a) The speed at t= 3s can be found by replacing t = 3s in the velocity equation.
v(3s) = (18m/s^2)*3s = 54m/s
b) the distance traveled by this time can be found by replacing t = 3s in the position equation.
p(3s) =(9m/s^2)*(3s)^2 = 81 m
c) first, we need to find what is the time when the position is equal to 200m.
p(t) = 200m = (9m/s^2)*t^2
√(200/9) s = t = 4.7s
Now we replace that time in the velocity equation and we get:
v (4.7s) = (18m/s^2)*4.7s = 84.6m/s
d) ok, to do this we know that.
1 hour has: 60*60 = 3600 seconds.
then we have the transformation k = 1h/3600s
1 km has 1000 meters.
then we have the transformation c = 1km/1000m
so we have that:
84.6m/s = 84.6m/s*(c/k) = 84.6*(3600/1000)km/h = 304.56 km/h
