Answer:
a)X=70.688m
b)v=18.8m/S
Step-by-step explanation:
the truck has constant speed while the car moves in uniformly accelerated motion
A body that moves with constant acceleration means that it moves in "a uniformly accelerated movement", which means that if the velocity is plotted with respect to time we will find a line and its slope will be the value of the acceleration, it determines how much it changes the speed with respect to time.
When performing a mathematical demonstration, it is found that the equations that define this movement are as follows.
Vf=Vo+a.t (1)\\\\
\frac{Vf^{2}-Vo^2}/{2.a} =X(2)\\\\
X=Xo+ VoT+0.5at^{2} (3)\\
Where
Vf = final speed
Vo = Initial speed
T = time
A = acceleration
X = displacement
In conclusion to solve any problem related to a body that moves with constant acceleration we use the 3 above equations and use algebra to solve .
For the automobile
we use the ecuation number 3
Xo=0
Vo=0
a=2.5
X=0.5(2.5)t^2
X=1.25t^2
for the truck
x=Vt
X=9.4t
the distance is the same we can match the previous equations
1.25t^2=9.4t
t=9.4/1.25=7.52s
using the ecuation for the truck
x=9.4*7.52=70.688m
b) for this point we can use the ecuation number 1 for automobile
Vf=Vo+at
Vf=0+2.5(7.52)
Vf=18.8m/S