September 17, 2014
Start-up Notes: Relative Velocity
Two cars approach each other. One car
is moving 1.0 m/s to the right. The other
is 10.0 m away from the first, has an
initial velocity of 6.0 m/s to the left, and
is slowing at a rate of 2.0 m/s2.
[1] Set up two separate position
equations for the two cars.
[2] Sketch position-time graphs for both
cars.
[3] Calculate when the cars will hit.
[4] Where do the cars collide (relative to
the first car's position)?
[5] Calculate the relative speed of the
cars at the moment of collision.
Start-up Notes: Relative Velocity
Two cars approach each other. One car
is moving 1.0 m/s to the right. The other
is 10.0 m away from the first, has an
initial velocity of 6.0 m/s to the left, and
is slowing at a rate of 2.0 m/s2.
[1] Set up two separate position
equations for the two cars.
[2] Sketch position-time graphs for both
cars.
[3] Calculate when the cars will hit.
[4] Where do the cars collide (relative to
the first car's position)?
[5] Calculate the relative speed of the
cars at the moment of collision.
September 17, 2014
Start-up Notes: Relative Velocity
Two cars approach each other. One car
is moving 1.0 m/s to the right. The other
is 10.0 m away from the first, has an
initial velocity of 6.0 m/s to the left, and
is slowing at a rate of 2.0 m/s2.
[1] Set up two separate position
equations for the two cars.
x=1/2at2 +v0t + x0
x=1t=t
x=1/2(2)t2–6t+ 10 = t2-6t+10
[2] Sketch position-time graphs for both
cars.
[3] Calculate when the cars will hit.
x=x
t=t2-6t+10
0=t2-7t +10
0=(t-2)(t-5)
t=2 seconds
[4] Where do the cars collide (relative to
the first car's position)?
x=1t = 1(2 seconds) = 2m
[5] Calculate the relative speed of the
cars at the moment of collision.
v=1 m/s
v=v0 + at = -6 + 2t = -2 m/s
Vrelative = 3 m/s