# Velocity word problems

The following velocity word problems will strengthen your knowledge of speed and velocity. In the end, the difference between speed and velocity should be clear.

Problem #1: Two cars are traveling on US 301 south to go to the same store that is 10 miles way.

Car #1 makes it 15 minutes.

Car #2 makes it in 15 minutes.

﻿Do the cars have the same average speed? How about velocity?

Since the cars make it at the same time, they must have the same average speed.

15 minutes is 0.25 hour, so average speed = 10 divided by 0.25

Average speed = 40 miles per hour.﻿

We know the cars are traveling in the same direction.﻿

However, just knowing the average speed is not enough information to conclude that the cars have the same velocity.

At some point, it is possible that the cars could have had the same instantaneous speed of 30 miles per hour. In this specific case, you can say that they had the same velocity.

## Challenging velocity word problems

Problem #2: A car going westward has a cruising speed of 50 miles per hour. Another car that is 10 miles away and traveling eastward has a cruising speed of 50 miles per hour.

1) Do both cars have the same speed ? 2) Do they have the same velocity ? 3) Do the cars have a constant velocity ? 4) How far will both cars be in half an hour after they pass each other? 5) After how long will the cars meet?

Solution :

1) The cars have the same speed since they are both traveling with a speed of 50 miles per hour.

2) The cars have different velocity since they are moving in opposite directions.

3) Each car has a constant velocity since the speed does not change while the car is cruising. Furthermore, the car is traveling in a straight line.

4)To get the distance, use the formula d = v × t

d = 50 × 0.5

d = 25 miles

Therefore, after half an hour both cars will be 25 miles away.

However, recall that they were 10 miles away from each other. This means that they will meet half way or after they have driven 5 miles. they will be 20 miles away after they pass each other. (25 - 5 = 20)

5) The formula to get the speed  is

Speed =
d / t

We need to find the time, so we must rewrite the speed formula.

If 4 =
20 / 5

Then, 5 =
20 / 4

By the same fashion,

If Speed =
d / t

Then, t =
d / speed

Since the cars are 10 miles away from each other, d = 10 miles.

However, if they maintain a constant velocity, they will meet half way or 5 miles. We know the speed is 50 miles per hour.

t =
d / speed

t =
5 / 50

t = 0.10 hour.

How many minutes is 0.10 hour ?

Just multiply 0.10 by 60 and you will get 6.

So the cars will meet in 6 minutes.

Problem #3: Your turn to solve a velocity word problem!
A car is driving on 95 south to go to New York that is 250 miles way. The car makes it to New York in 5 hours. Did the car have a constant velocity?

If you cannot solve this problem, try reading again the solution to the two velocity word problems above.

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

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