Motion Calculation Reference Guide

Jim is running across the lawn and back, he then turns around and runs back at 10 miles per hour South. It takes him 20 seconds to reach one end, and 10 seconds to get back. What is his velocity on the way there?

5 miles per hour North

What is the difference between distance and displacement?

Distance is the total length of the actual path between two points. Displacement is the length and direction of a straight line between starting and ending points.

A train car is moving 30 miles per hour west. A person on the train is walking 2 miles per hour west. How fast does it look like the person is moving to someone on the side of the train?

30+2=32 miles per hour

A train car is moving 30 miles per hour west. A person walks on the train car 2 miles per hour East. How fast does it look like the person is moving to a bystander?

30-2= 28 miles per hour East.

Eddie is mowing the lawn at a speed of 3 miles per hour, and is heading north. Then, he turns around and mows back at the same speed. What is his velocity? Speed+Distance

3 mph South

Bob is running a 10 mile race while running at a constant speed of 4 miles per hour. How long does it take Bob to finish? T=D/S

10/4=2.5 It takes him 2.5 hours to run the race

Jimmy is running around the track at a constant speed of 10 miles per hour. It takes him 0.5 hours to complete his goal. How far does he run? D=SxT

10x0.5=5 He runs 5 miles.

Arjuna is running 2 miles per hour North. It takes him 1 minute to reach the end of the road before he turns around. His final velocity is 2 miles per hour, and he accelerates at a rate of 0 mí/hr/s. What is his final velocity?

2 miles per hour South

Timmy rode his bike 2 miles in 20 minutes. What was Timmy's speed? S=D/T

2/20=0.1 miles per minute or 0.1x60=6 miles per hour

A car is driving at a constant speed of 20 miles per hour, It then decides to speed up to 60 miles per hour in 5 seconds. What is the acceleration of the car? Acceleration = Change in speed/time

60-20=40 40/5=8 12 miles/per hour/per second

Velocity

Speed with direction

Person A is sitting on a sidewalk. Person B and person C go by on a bus moving 100 miles per hour East. Person B stays seated while person C gets up on the bus and walks 5 miles per hour East. How fast are the people moving according to Person A?

Person B looks like he is moving 100 mph, and person C looks like they are moving 105 mph.

Speed

The distance an object travels in a certain amount of time

Billy runs one full lap around the track and ends at the same place that he started. What is his distance and displacement?

The distance is however long one lap around the track is. The displacement is 0 because he ends at the same spot.

Displacement

The overall difference in position from start to finish

Acceleration

The rate of change in speed compared to time

Distance

The total length of the path taken by an object