v: average speed, average velocity

d: distance, displacement

t: elapsed time

Variable

Abbreviation

Units

Direction required?

Vector or Scalar?

Examples

Speed

v

distance/time

No direction

Scalar

m/sec

22 cm/yr

Velocity

v

distance/time

With direction

vector

m/sec north,

36 km/hr west

Distance

d

distance

No direction

Scalar

15m

30.0 km

Displacement

d

distance

With direction

Vector

546 km down

24.9 m west

Time

t

Time

No direction

Scalar

15 sec

32 days

When solving velocity problems, "d" can mean either distance or displacement depending on the context of its use. Likewise, the variable "v" can stand for either speed or velocity, depending on how it is used. Direction, when given, can appear in a number of formats. A direction may be given as a compass direction, such as 270degrees, or as a relative direction such as up, down, left or right.

When solving velocity problems you will use the equation v= d/t this equation is read as " velocity equals displacement divided by time".

Velocity problems are usually expressed a real world word problems. Here is an example:

1. Identify the information given in the problem. **d=160km, t=1.6h, v=?**

2. Set the problem up in 3 steps, step 1: write down the equation:

step 2: substitute the values and units of measurement:

step 3: Solve the problem and record the answer with the proper units:

2. Set the problem up in 3 steps, step 1: write down the equation:

step 2: substitute the values and units of measurement:

step 3: Solve the problem and record the answer with the proper units:

In some speed and velocity problems you will have to rearrange the velocity equation to solve for the displacement, or time. To solve for **displacement** use this form of the equation. **d=v ****ยท**** t**

To solve for the time use **t=d / v**

Here is an example problem that solves for distance ( or displacement).

While in orbit, the speed of the Space Shuttle is about 27 200km/h. At this speed, how far can the Space Shuttle travel in .25h. Here is how the problem is solved.

Note that the time unit , "h" cancels out leaving only the distance unit in the answer.

Here is an example problem solving for time.

The SR-71 Blackbird can cruse at 3600km/h. At this velocity, how long would it take the Blackbird to fly from Myrtle Beach to Charleston, a distance of 160km? Here is the solution.

Note that km cancels out leaving the unit of the answer, hours. **Click Here for some velocity problems you can work. Bring your answers to class. See Mr.D. for the solution sheet.**

Constant velocity: Let's suppose that a car is dripping oil at the rate of one drop per second. Now let's suppose that the car is moving with a constant velocity from left to right. Since the car is moving with a constant velocity, it travels the same distance during every second of motion. The pattern of oil drops you would expect to see on the road after the car passed would look something like this:

Note that the drops are all the same distance apart. This tells you that the velocity of the car is constant.