Consider the following problem. Vehicle 1 and Vehicle 2 each move in a straight line. At time
t=0
t
0
,
Vehicle 1 starts from position 0 with initial velocity 0 and constant acceleration aa. At the same time, Vehicle 2 starts from position
s
0
s
0
and travels with constant velocity vv. The position of Vehicle 1 is given by the equation
s=12at2
s
1
2
a
t
2
(1)
The position of Vehicle 2 is given by the equation
s=vt+
s
0
s
v
t
s
0
(2)
For given values of
a
a,
v
v,
and
s
0
s
0
,
at what time
t
t
will Vehicle 1 to overtake Vehicle 2? At what position will this happen? Plot your solution for
t
t
as a function of
a
a
with
v=80 ft/s
v
80 ft/s
and
s
0
=4000 ft
s
0
4000 ft
.
For given values of
v
v
and
s
0
s
0
,
what value of
a
a
would cause Vehicle 1 to overtake Vehicle 2 at a given time
t
t?
Plot your solution for
a
a
as a function of
t
t
with
v=80 ft/s
v
80 ft/s
and
s
0
=4000 ft
s
0
4000 ft
.