Motion is Relative Motion does not exist isolated by itself. Motion must be defined in terms of some frame of reference, which is to say that motion is relative to that frame.

At Rest? This person is “standing still” on the ground. Are they at rest? Yes, if the motion is defined relative to the ground then the person is at rest with respect to the ground. That means the distance between the person and a point on the ground is not changing.

Or Not? But the same person is not at rest with respect to the Sun. The person is moving at the same speed as the Earth relative to the Sun. So it is possible to have a different speed depending on which frame of reference is chosen.

Bus Ride Passenger Driver What is the speed of the passenger? Relative to the driver the passenger is at rest, since both stay in the same position relative to each other. Relative to the ground the passenger is moving at the same speed as the bus however.

Race Track 30 m/s The speed of the red car relative to the ground is 30 m/s. The speed of the green car relative to the ground is 24 m/s. The speed of the red car relative to the green car is 6 m/s. That is to say it is moving away from the green car 6 meters every second. 24 m/s

Drag Race 30 m/s 24 m/s Problem: The two cars from the previous slide start side by side and race down a race track. At what time is the red car 120 m ahead of the green car? One approach to solving the problem is to calculate the distance for the red car as d= 30m/s(t) and the distance for the green car as (d-120m) = 24m/s(t). Next solve the second equation for d, or d= 24m/s(t) + 120m. One can then set the two right sides of the equations for d equal to each other and solve for t. It is simpler to use the relative speed between the two cars, however. If the cars are separated by 120m then 120m = 6 m/s (t), or t = 20 s.

Adding Motion 10 m/s 20 m/s A ball is thrown forward from a car at a speed of 10m/s relative to the car. The car is moving at 20 m/s relative to the ground. What is the speed of the ball relative to the ground? In this case one can simply add the the two speeds and find the answer is 30 m/s.

Einstein 3x108 m/s 20 m/s Now look at the light leaving the headlight of the same car. It is moving at 3x10^8 m/s relative to the car. The car is moving at 20 m/s relative to the ground. Is the speed of light now more than 3x10^8 m/s? It turns out the answer is NO! Light appears to move at 3x10^8 m/s relative to every object, no matter how fast that object is moving itself (up to a limit, which is 3x10^8m/s). This is one of the postulates of Einstein’s Special Theory of Relativity.

Time One of the consequences of Einstein’s Theory is that time is not the same for every object. The faster an object moves, the slower time appears to pass for it, at least from the point of view of an observer at rest relative to the object’s frame of reference.