FIRST SECTION
You should use the formula for uniformly accelerated linear movement.
Initial speed is 0 because it starts from rest.
d=(1/2)at^2+vot =(1/2)(4.0 m/s^2)(3s)^2+03s=(1/2)(4.0 m/s^2)3^2s^2+0=2.0 m9=18m
You can calculate the final speed with the other formula:
v=at+vo=(4.0 m/s^2)(3s)+0=(4.0 m/s)(3)=12m/s
SECOND SECTION
You should use the formula for uniform linear movement.
Velocity is a constant: it remains in 12m/s.
d=vt=12m/s2s=12m2=24m
THIRD SECTION
We should use the same formulas as the first section, but with different numbers.
Initial velocity will be 12m/s, and then velocity will start to decrease until it gets to 0.
We don’t know what the time is for this section.
Acceleration is negative, because it’s slowing down.
v=at+vo
0=-3.0 m/s^2t+12m/s
3.0 m/s^2t=12m/s
t=(12m/s)/(3.0 m/s^2)=4(1/s)/(1/s^2)=4s^2/s=4s
Now let’s use that time in the other formula:
d=(1/2)at^2+vot =(1/2)(-3.0 m/s^2)(4s)^2+(12m/s)3s=(-1.5 m/s^2)4^2s^2+123ms/s=-1.5 m4^2+36m=-1.5*16m+36m=-24m+36m=12m
Now let’s add the 3 stages:
d=18m+24m+12m=54m
