EOM: Speed and Velocity

The Valdez family traveled from New York City to Washington, DC. They left at 12:00 p.m., traveled 95 miles, and stopped to eat in Philadelphia. They continued driving another 135 miles and arrived in Washington, DC, at 5:00 p.m. What was the family’s average speed?

• 19 mph

• 27 mph

• 46 mph

• 230 mph

Answer explanation

The total distance traveled is 95 miles + 135 miles = 230 miles. The total travel time is from 12:00 p.m. to 5:00 p.m., which is 5 hours. Average speed = total distance / total time = 230 miles / 5 hours = 46 mph. The correct answer is 27 mph.

A student is driving her car to college in the fall. It takes 7.5 hours to travel a distance of 338 miles. What is the average speed of the car? Round to the nearest whole number.

• 60 miles per hour

• 45 miles per hour

• 55 miles per hour

• 50 miles per hour

Answer explanation

To find the average speed, divide the total distance by the total time. Average speed = 338 miles / 7.5 hours = 45.07 miles per hour, which rounds to 45 miles per hour. Thus, the correct answer is 45 miles per hour.

Liam, Jackson, and Ethan are racing remote-controlled cars around a track 2.0 kilometers in length. The cars travel at a constant speed. The table below shows the finish time for each car. Car | Finish Time (hour) S | 0.028 T | 0.031 U | 0.033 V | 0.035 What was the velocity of the winning car when it crossed the finish line? Round to the nearest whole number.

• 71 km/h south

• 71 km/h west

• 61 km/h north

• 57 km/h south

Answer explanation

To find the velocity of the winning car (Car S), use the formula: velocity = distance/time. The distance is 2.0 km and the time is 0.028 hours. Thus, velocity = 2.0 km / 0.028 h = 71.43 km/h, rounded to 71 km/h south.

James wanted to see if his speed would change on different track surfaces. He ran at a comfortable pace on grass, gravel, concrete, and turf. He measured the amount of time it took to run 1,000 meters. Track Distance (meters) Time (minutes) Grass 1,000 6.2 Gravel 1,000 5.7 Concrete 1,000 5.0 Turf 1,000 5.5 What is the average speed of the fastest track? Round to the nearest whole number.

• 161 m/min

• 175 m/min

• 200 m/min

• 182 m/min

Answer explanation

To find the average speed, use the formula: speed = distance/time. For concrete, the time is 5.0 minutes. Thus, speed = 1000 meters / (5.0 minutes * 60 seconds/minute) = 200 m/min. This is the fastest speed.

Samuel kicks a soccer ball, and it travels at a rate of 10 m/s. Then, Kai kicks it again at a speed of 15 m/s. The diagram below shows the direction the ball is moving before and after the second kick. Which of the following statements correctly identifies what is happening to the speed and velocity of the soccer ball?

• Speed changing, velocity changing

• Speed constant, velocity constant

• Speed changing, velocity constant

• Speed constant, velocity changing

Answer explanation

The soccer ball's speed changes from 10 m/s to 15 m/s after Kai's kick, indicating a change in speed. Additionally, the direction of the ball changes, which means the velocity is also changing. Thus, the correct choice is 'Speed changing, velocity changing'.

Ava travels west for 3 hours and has a displacement of 135 miles. Michael travels west for 5 hours and has a displacement of 135 miles. Which of the following correctly identifies the similarities between the motion of Ava and Michael?

• A. speed

• B. distance

• C. time

• D. velocity

• E. direction

Answer explanation

Both Ava and Michael traveled the same distance of 135 miles west. While their speeds and times differ, the distance and direction of their travel are the same, making options B (distance) and E (direction) correct.

Aria is driving her car and wants to understand the difference between speed and velocity. The table below lists the characteristics of speed and velocity. Identify the correct label described in each column for Aria's understanding. Write the answers in the correct boxes.

• Speed: Distance, Time Velocity: Distance, Time, Direction

• Speed: Distance, Time, Direction Velocity: Distance, Time

• Speed: Time, Direction Velocity: Distance, Time

• Speed: Distance, Direction Velocity: Time, Direction

Answer explanation

Speed is defined as the distance traveled over time, while velocity includes both distance and direction. Therefore, the correct labels are: Speed: Distance, Time and Velocity: Distance, Time, Direction.

Nia walks on a field at a constant speed. She starts at point X and heads north. It takes her 57 seconds to walk from point X to point Z.

• 1.4 m/s east

• 1.4 m/s west

• 1.4 m/s north

• 1.4 m/s south

Answer explanation

Nia walks north from point X to point Z, taking 57 seconds. Since her direction is north, the correct speed is 1.4 m/s north.

Nia walks on a field at a constant speed. She starts at point X and heads north. It takes her 57 seconds to walk from point X to point Z. What is Nia’s displacement from Point X to Point Z?

• 20 m

• 30 m

• 50 m

• 80 m

Answer explanation

Nia's displacement is the straight-line distance from point X to point Z. Since she walks north for 20 m in 57 seconds, her displacement is 20 m, making the correct answer 20 m.

What is the speed at Point A? Distance: 20 cm, Time: 0.32 s.

Answer explanation

To find the speed at Point A, use the formula: speed = distance / time. Here, speed = 20 cm / 0.32 s = 62.5 cm/s. Thus, the speed at Point A is 62.5 cm/s.