Average Velocity Practice Problems

On an ordinary day, you walk from the park to the recreational center at an average speed of 5.4 kph (kilometers per hour), and the round trip takes you 1 h and 30 min. One day, instead of walking, you decide to jog, hence increasing your speed to 10 kph. How much longer does the slower trip take?

A rushing ambulance which is carrying an injured patient is approaching the hospital with a distance from the accident scene defined by x(t) = bt² - ct³, where b = 3.10 m/s² and c = 0.147 m/s³. Determine the average velocity of the ambulance for t = 0 to t = 7.0 s.

A dog has escaped from its cage and has run 8.2 km away towards a park. The dog has returned to its cage after it has escaped. The dog has taken 25 minutes to run from the park back to the cage. If the origin is positioned at the cage and the dog has run towards the +x-axis, what was the dog's average velocity in m/s for its return from park to the cage?

During your lunchtime in school, you decided to go out and went 70 m south to a coffee shop, and ordered your favourite coffee. Then you walked 40 m due north to a park, where you sat and enjoyed your coffee. It took you 55.0 s to walk from the school to the coffee shop and then 72.0 s to walk from the coffee shop to the park. Determine your average velocity and average speed for the duration of your lunch break. Consider the motion in the south direction to be positive.

Imagine you are on a train, moving at a constant speed of 90.0 km/h. You closed your eyes for 10.0 seconds. How far does the train travel during this short time?

At t₁ = 1.5 s, an object is situated at a position x₁ = 12.3 m, and at t₂ = 7.8 s, it's found at x₂ = 25.6 m. i) Determine the object's average velocity throughout this time span. ii) Is it possible to ascertain its average speed based on these data? Provide an explanation for your answer.

A shooter fires a bullet, and it travels through the air at a constant speed. The bullet covers a distance of 210 m. The shooter hears the echo of the bullet hitting a distant target 14.5 seconds after firing it. Assuming the speed of sound is 340 m/s, what is the speed of the bullet when it leaves the gun?

A car accelerates from rest and covers a distance of 120 m in 15s. It then turns and travels halfway back in 4.0 s. Calculate the car's average speed during the entire journey.

A car's position along a straight road as a function of time is shown in the figure below. What is the car's average velocity between t = 15.0 s and t = 35.0 s?

Over the course of a year, a space station travels approximately 10¹² km as it orbits the Earth. What is the average speed of the space station in kilometers per hour (km/h) during its journey around the planet?

Consider a train that initially travels 1.50 × 10³ miles at a speed of 180 mph. It then reduces its speed to 120 mph for the subsequent 3.00 × 10³ miles. Determine i) the journey's total duration and ii) the train's average speed (in mph) for the entire trip.

At t₁ = 1.50 s, an object is situated at a position x₁ = 12.3 m, and at t₂ = 7.80 s, it's found at x₂ = 25.6 m. i) Determine the object's average velocity throughout this time span. ii) Is it possible to ascertain its average speed based on these data?

Consider a copper wire that is being rolled into a circular coil. The copper wire starts coiling at an inner radius of 4.8 dm and finishes at an outer radius of 9.3 dm. Each coil is separated by a distance of 2.2 mm. Find the total length of the copper wire.

Two bikes are to reach a destination simultaneously. Both start at the same time and are at an equal distance from the destination. They both travel in straight lines toward it. Bike P has variable average velocities: 30 km/h for the first 80 km, 45 km/h for the next 50 km, and then back to 30 km/h for the remaining 100 km. The bike T maintains a constant velocity throughout the journey. Determine the speed of the bike T to ensure that both bikes arrive at the same time.

Consider a nanosheet-based memory device, digital bits of information are encoded on it. Each bit occupies a space of about 1.2 nm. The readout mechanism scans along the nanosheet sequence of bits at a constant speed of about 1.1 m/s. Find the number of digital bits that the readout mechanism scans every second.

Mark starts his bike from his office at 5.30 p.m., moves at a constant speed towards the east for 5 minutes, takes a U-turn at 2800 m and drives at the same constant speed towards his house which is 4500 m from the U-turn. He reached his house at 5.50 p.m. Determine the average velocity of Mark's bike during these two intervals.

Brian starts in his car from his house at 8.20 a.m., moves at a constant speed towards the east for 2 minutes, takes a U-turn at 400 m and drives at the same constant speed towards the supermarket which is 1500 m from the U-turn. He reached the supermarket at 8.30 a.m. Determine the average velocity of Brian's car for the whole trip.

Matt decides to go for a family picnic on the weekend. The picnic spot is 150 miles from their house. During their onward journey, they drive with a speed of 45 mph for 100 miles and a speed of 70 mph for the rest of the journey. During their return, they cover 90 miles at a speed of 50 mph and a speed of 65 mph for the remaining distance. Determine the average speed of their vehicle on the return journey.