Kinematic Relationship between time displacement velocity acceleration Relationships

Kinematic Relationship between time, displacement, velocity, acceleration.

Relationships between the variables (s, d, t) This is the scalar relationship between speed, distance, and time. s = speed d = distance t = time speed = distance / time s=d/t

A car traveled 300 miles in 10 hours, determine the speed of the car.

distance = 300 miles time = 10 hours s = distance / time = 300 miles / 10 hours = 30 miles / hr.

Relationships between the variables (v, d, t) This is the vector relationship between velocity, displacement, and time. v = velocity d = displacement t = time velocity = displacement / time

A car traveled 300 miles north in 10 hours, determine the velocity of the car. displacement = 300 miles time = 10 hours Velocity = displacement / time = 300 miles / 10 hours = 30 miles / hr. north

Variations on the same equation speed = distance / time distance = speed • time = distance / speed velocity = displacement / time displacement = velocity • time = displacement / velocity

units Units of speed m/s km/hr (kph) ft/s miles/hr (mph) Units of velocity m/s north km/hr west ft/s south miles/hr east

How units are related speed = distance / time distance meters time seconds speed = meters / seconds

How units are related distance = speed • time speed - meters / seconds time - seconds distance = meters / seconds • seconds = meters

How units are related time = distance / speed distance = meters speed = meters / seconds time = meters / (meters / seconds) = seconds

Another way to calculate for velocity is to use an object’s position with respect to time. When the object is at point A, its position is 2 meters after 3 seconds and point B is 5 meters after Displacement (m) Position and average velocity B (8, 5) rise A (3, 2) run Time (s)

Position and velocity Think of slope where we have

When the object is at point A, its velocity is 2 m/s after 3 seconds and point B is 5 m/s after 8 seconds. Velocity (m/s) Velocity and average acceleration B (8, 5) rise A (3, 2) run time (s)

Velocity and acceleration Think of slope where we have

Practice problems 1. A person was running south at a rate of 3 m/s. This person has been running for 3 minutes. How far has this person traveled in the 3 minutes?

2. During the first 10 seconds, a car traveled a distance of 800 meters. What is the average speed of the car?

3. If the cheetah has been running at a speed of 30 m/s for 8 seconds, how far has the cheetah traveled in this span of time?

4. A car slows from a velocity of 40 m/s to 25 m/s in 8 seconds. What is the average acceleration of the car?

5. If the average acceleration of an object is 3 m/s 2 over a span of time of 2 seconds, what is the change in velocity over the 2 seconds?