Motion Without Acceleration

| Multimedia | Practice Homework | Homework |

Context

An object can continue to move at a constant speed or the speed can change as it moves along.

What do we mean by motion without acceleration?

When an object moves at the same speed it is motion without acceleration.

Explanation

There are several ways to say Newton's first law. You may be familiar with the following version:

An object in motion will remain in motion unless acted upon by an outside force and an object at rest will remain at rest unless acted upon by an outside force.

Another version for the motion part is:

An object will continue in a continuous, straight-line, constant speed motion until acted upon by an unbalanced force.

There are some everyday examples of this. A marble rolled on a level table will usually keep going until it hits something. Air hockey pucks keep going until they hit something. Ice skaters keep going until they hit something or dig into the ice. Space ships keep going in straight lines and have to use their thrusters to change direction.

This section will help you:

• Understand the relationships among distance, speed, and time when there isn't any acceleration.
• Learn how to calculate distance, speed, and time when there isn't any acceleration.

Model

We will have to agree on some terminology before we can continue. Objects are at a well defined position at any given instant. As an object moves from one position to another it travels a distance that can be found by measuring how far apart the first position is from the second position. The speed is defined as the change in distance with respect to time. If the positions are 1.5 meters apart after 1 second, the speed would be 1.5 m/sec (1.5 meters per second). You may be more familiar with 50 mph (50 mi/hr or 50 miles per hour). In that case the distance of 50 miles is traveled in one hour.

Speed is closely related to velocity. Velocity is speed in a specified direction. In other words the speed is the amount or magnitude of the velocity. 50 mph is a speed, 50 mph toward the North is a velocity.

Galileo laid the groundwork for Newton's first law. He came up with the notion of inertia or the tendency for objects to remain in motion. A good web page that explains this is http://id.mind.net/~zona/mstm/physics/mechanics/forces/galileo/galileoInertia.html. Today we think of inertia as just another way to express Newton's first law.

When there is no acceleration the speed is constant and the final velocity is equal to the initial velocity. In symbols that could be written as v_f = v_i. The distance traveled can be obtained by multiplying the speed times the time. You may be familiar with the expression that the distance is equal to the rate times the time. In symbols this could be written as d = r*t, where d is distance, r is rate (or speed or velocity when it has a direction), and t is time. The equation is most commonly written with velocity:

d = v*t     or     d = vt

Practice problem: What is the velocity of someone who travels 16,000 m in 3600 sec?

v = d/t = 16,000 m/3600 sec = 4.4 m/sec (about 10 mi/hr)

Thinking Questions

1. Can you have a speed without a velocity?
2. Can you have a velocity without a speed?
3. Is the distance directly or inversely proportional to the time?