Confused about finding acceleration from this info?

Question

It starts from rest and travels 40 m in 3 seconds. I know accel = v-vo/time. But I don't get how to get that stuff. So how would I find accel and velocity and vo from this info

earlier someone said 80 as final velocity, I don't get how you would get 80 as final velocity

Answer 1

S - Distance.
U - Initial velocity.
t - time taken.
a - acceleration.

Using the formula: S = ut + ½at²
S = ut + ½at²
S - ut = ½at²
2(S - ut) = at²
{2(S - ut)} /t² = a
{2(40 - 0*3)} /3² = a
2(40) /9 = a
80 /9 = a
a = 8∙888..m/s²

Velocity is speed measured in a given direction, so it's a combination or two things.
The initial velocity (Vo) is zero - information given, direction not stated.
Final velocity V:
a = (v - u)/t
at = v - u
v = at + u
v = (8∙888..)(3) + 0
v = 26∙666...m/s.

Answer 2

Initial velocity is zero because it starts from rest. You are not given the final velocity, so you must use another equation. You have the distance and the time. If we assume a constant acceleration, we can use calculus to get an answer.

Integrating twice gives 1/2*a*t^2+vo*t=d where d is distance, vo is initial velocity, t is time, and a is acceleration. vo is zero, so the acceleration is twice the distance, divided by the square of the time. a=2d/(t^2) This is 80 meters by nine square seconds, or 8.8888 meters per second squared.

Answer 3

X=Xo + Vo t + 1/2 a t^2

Xo=0 (this is my x-reference)
Vo=0 (starts from rest)

so X = 1/2 a t^2

a= 2X / t^2

a= 80m / 9s^2 = 8.88 m/s2

BTW final speed will be 26.66 m/s