Worksheet: Average Speed and Velocity

In this worksheet, we will practice calculating the average speed or velocity of an object referring to the variation of their distances or displacements with time.

Q1:

An airplane leaves Chicago and makes the 3.00×10-km trip to Los Angeles in 18.0×10 s. A second plane leaves Chicago 1.80×10 s later and arrives in Los Angeles at the same time. Find the ratio of the average velocities of the two planes. Ignore the curvature of Earth and the difference in altitude between the two cities.

Q2:

A sonar echo returns to a submarine 1.20 s after being emitted. Find the distance to the object creating the echo. Use a value of 1,540 m/s for the speed of sound in sea water.

Q3:

If the Sun suddenly stopped shining, we would not know that until just after the last light that the Sun had emitted arrived at the Earth. Find how long it would take for this light to reach the Earth. Use a value of 1.496×10 m for the distance from the Earth to the Sun and use a value of 3.00×10 m/s for the speed of light in a vacuum.

Q4:

A city and an international airport are 46 km away from each other. A maglev train takes 11 minutes to travel between them. What is the maglev train’s average speed?

Q5:

A Little League baseball player pitches a baseball at 33 km/h. At that speed, how long does it take a ball thrown by this player to reach the home plate, 14 m away from the pitcher’s mound?

Q6:

A dog runs 33 m to the east in 9.0 s, then turns and runs 13 m to the west in 4.3 s. Assume movement to the east corresponds to positive displacement.

What is the average velocity of the dog?

What is the dog’s average speed?

Q7:

A particle moves in a straight line at a constant speed of 30.0 m/s. What is the displacement of the particle between the times 𝑡=0.00 s and 𝑡=5.00 s?

Q8:

On February 15, 2013, a superbolide meteor (one that is brighter than the Sun) entered Earth’s atmosphere over Chelyabinsk, Russia, and exploded at an altitude of 23.5 km. The blast wave took 2.50 minutes to reach ground level.

What was the speed of the blast wave?

What was the ratio of the speed of the blast wave to the typical value of the speed of sound at sea level, 343 m/s?

Q9:

A cyclist rides 4.7 km east for 17 minutes. He then heads west for 11 minutes, riding 2.9 km. Finally, he rides east for 13 km, which takes 51 minutes. Assume that riding westward corresponds to positive displacement.

What is the final displacement of the cyclist from their starting point?

What is the cyclist’s average velocity?

Q10:

A dragster has an acceleration of 26.0 m/s2. What is the speed of the dragster after it has moved a distance of 402 m while accelerating at this rate, starting from rest?

Q11:

An airplane lands with an initial velocity of 70.0 m/s and then decelerates at 1.50 m/s2 for 40.0 s. What is its final velocity?

Q12:

The diagram shows a graph of the variation of the position 𝑥 of an object with time 𝑡.

What is the velocity of the object in the time interval 𝑡>0 s to 𝑡=0.5 s?

What is the velocity of the object in the time interval 𝑡>0.5 s to 𝑡=1.0 s?

What is the velocity of the object in the time interval 𝑡>1.0 s to 𝑡=2.0 s?

Q13:

The distance from a university to a student’s home is 10 miles and it usually takes the student 20 minutes to drive this distance. Calculate the student’s average driving speed in meters per second.

Q14:

Suppose you drop a rock into a dark well and, using precision equipment, you measure the time for the sound of a splash to return. The sound returns after 2.000 s.

Neglecting the time required for sound to travel up the well, calculate the distance to the water.

Now calculate the distance taking into account the time for sound to travel up the well. The speed of sound is 332.00 m/s in this well.

Q15:

The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model, you can view hydrogen, the simplest atom, as having a single electron in a circular orbit 1.06×10 m in diameter. If the average speed of the electron in this orbit is known to be 2.20×10 m/s, calculate the number of revolutions per second it makes about the nucleus.

  • A 3 . 3 0 × 1 0 rev/s
  • B 6 . 6 1 × 1 0 rev/s
  • C 2 . 0 8 × 1 0 rev/s
  • D 1 . 0 4 × 1 0 rev/s
  • E 4 . 4 5 × 1 0 rev/s

Q16:

A football quarterback runs 17.0 m straight down the playing field in 3.50 s. He is then hit and pushed 2.00 m straight backward in 1.15 s. He breaks the tackle and runs straight forward another 24.0 m in 6.20 s. Calculate his average velocity for the entire motion.

Q17:

Conversations with astronauts on the lunar surface were characterized by a kind of echo in which the earthbound person’s voice was so loud in the astronaut’s space helmet that it was picked up by the astronaut’s microphone and transmitted back to Earth. It is reasonable to assume that the echo time equals the time necessary for the radio wave to travel from Earth to the Moon and back (i.e., neglecting any time delays in the electronic equipment). Calculate the distance from Earth to the Moon given that the echo time was 2.56 s and that radio waves travel at the speed of light (3.00×10 m/s). Give your answer in kilometers.

  • A 3 . 8 4 × 1 0 km
  • B 3 . 0 0 × 1 0 km
  • C 1 . 1 7 × 1 0 km
  • D 3 . 8 4 × 1 0 km
  • E 7 . 6 8 × 1 0 km

Q18:

The speed of propagation of the action potential (an electrical signal) in a nerve cell depends, inversely, on the diameter of the axon (nerve fiber). If the nerve cell connecting the spinal cord to your feet is 1.2 m long and the nerve impulse speed is 19 m/s, how long does it take for the nerve signal to travel this distance?

Q19:

Tidal friction is slowing the rotation of Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many years will pass before the radius of the Moon’s orbit increases by 1.92×10 m?

  • A 4 . 8 0 × 1 0 years
  • B 4 . 8 0 × 1 0 years
  • C 4 . 8 0 × 1 0 years
  • D 4 . 8 0 × 1 0 years
  • E 4 . 8 0 × 1 0 years

Q20:

On, May 26, 1934, a streamlined stainless steel diesel train called the Zephyr set the world’s nonstop long-distance speed record for trains. Its run from Denver to Chicago took 13 hours, 4 minutes, and 58 seconds, and was witnessed by more than a million people along the route. The total distance traveled was 1633.8 km.

What was its average speed in kilometers per hour?

What was its average speed in meters per second?

Q21:

Land west of the San Andreas fault in southern California is moving at an average velocity of about 8 cm/yr northwest relative to land east of the fault. Los Angeles is west of the fault and thus may some day be at the same latitude as San Francisco, which is east of the fault. How far in the future will this occur if the displacement to be made is 610 km northwest, assuming the motion remains constant? Give your answer in years.

  • A 7 . 6 × 1 0 yr
  • B 7 . 6 × 1 0 yr
  • C 7 . 6 × 1 0 yr
  • D 7 . 6 × 1 0 yr
  • E 7 . 6 × 1 0 yr

Q22:

The continents of North America and Europe are moving apart at a rate of about 3.0 cm/yr. At this rate, how long will it take them to drift 500 km farther apart than they are at present? Give your answer in years.

  • A 1 . 7 × 1 0 years
  • B 1 . 7 × 1 0 years
  • C 1 . 7 × 1 0 years
  • D 1 . 7 × 1 0 years
  • E 1 . 7 × 1 0 years

Q23:

A helicopter blade spins at exactly 140 revolutions per minute. Its tip is 5.00 m from the center of rotation.

Calculate the average speed of the blade tip in the helicopter’s frame of reference. Give your answer in meters per second.

What is its average velocity over one revolution? Give your answer in meters per second.

Q24:

Earth orbits the Sun at a distance of approximately 1.5×10 km.

Assuming that Earth has a circular orbit, what is Earth’s average orbital speed around the Sun? Give your answer in meters per second.

  • A 2 . 9 × 1 0 m/s
  • B 2 . 9 × 1 0 m/s
  • C 3 . 0 × 1 0 m/s
  • D 3 . 0 × 1 0 m/s
  • E 3 . 0 × 1 0 m/s

What is the average velocity of Earth relative to the Sun over a period of one year? Give your answer in meters per second.

Q25:

The position function of a particle is rijk(𝑡)=2.0𝑡+(2.0+3.0𝑡)+5.0𝑡m.

What is the particle’s instantaneous velocity at 𝑡=2.0s?

What is the particle’s instantaneous speed at 𝑡=2.0s?

What is the particle’s average velocity between 𝑡=1.0s and 𝑡=3.0s?

  • A ( 5 . 0 + 8 . 0 + 3 . 0 ) i j k m/s
  • B ( 3 . 0 + 5 . 0 + 8 . 0 ) i j k m/s
  • C ( 8 . 0 + 5 . 0 + 3 . 0 ) i j k m/s
  • D ( 8 . 0 + 3 . 0 + 5 . 0 ) i j k m/s
  • E ( 5 . 0 + 3 . 0 + 8 . 0 ) i j k m/s

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