Worksheet: Average Velocity

In this worksheet, we will practice calculating the magnitude of the average velocity of a particle moving in a straight line.

Q1:

The table shows the distance covered by a runner at certain times. How far did the runner travel in the first 86 seconds?

Time in Seconds 0 20 40 60 80 100
Distance in Metres 0 50 100 150 200 250

Q2:

A body, moving in a straight line, travelled 91 m at 8 m/s. Following this, it travelled at 11 m/s in the same direction for a further 13 seconds. Find the average velocity during the whole trip.

Q3:

A cyclist travelled 36.5 km from point 𝐴 to point 𝐡 at 36.5 km/h, and then he travelled a further 22 km in the same direction at 22 km/h. Given that ⃑ 𝑛 is a unit vector in  𝐴 𝐡 direction, determine the cyclist’s average speed 𝑣 and average velocity ⃑ 𝑣 during the whole trip.

  • A 𝑣 = 1 1 7 / k m h , ⃑ 𝑣 = ο€Ή 1 1 7 ⃑ 𝑛  / k m h
  • B 𝑣 = 2 9 . 2 5 / k m h , ⃑ 𝑣 = ο€Ή 7 . 2 5 ⃑ 𝑛  / k m h
  • C 𝑣 = 1 1 7 / k m h , ⃑ 𝑣 = ο€Ή 2 9 ⃑ 𝑛  / k m h
  • D 𝑣 = 2 9 . 2 5 / k m h , ⃑ 𝑣 = ο€Ή 2 9 . 2 5 ⃑ 𝑛  / k m h

Q4:

Given that the table shows the relation between the distance a runner can run and the time it would take him to run that distance, determine how long it would take him to cover a distance of 336 metres.

Time in Seconds 0 2 4 6 8 10
Distance in Meters 0 8 16 24 32 40

Q5:

The graph represents the distance traveled by a speed boat. Use the graph to determine, in miles per hour, the rate of change in distance.

Q6:

A moving particle reached a point 𝐴 ( βˆ’ 3 , 8 ) after 2 seconds and another point 𝐡 ( 5 , 0 ) after 10 seconds. Find the magnitude of the average velocity of the particle 𝑣 and the direction of the average velocity πœƒ .

  • A 𝑣 = √ 2 length units/second, πœƒ = 1 3 5 ∘
  • B 𝑣 = √ 2 length units/second, πœƒ = 4 5 ∘
  • C 𝑣 = 8 √ 2 length units/second, πœƒ = 2 2 5 ∘
  • D 𝑣 = √ 2 length units/second, πœƒ = 3 1 5 ∘
  • E 𝑣 = 2 √ 5 length units/second, πœƒ = 2 9 6 ∘

Q7:

The figure below shows the relation between time and the distance from a fixed point of a cyclist who is moving in a straight line. Using this information, find the magnitude of the average velocity vector of the cyclist.

  • A 3 m/s
  • B 11 m/s
  • C 10 m/s
  • D 5 m/s

Q8:

A person drove a car for 723 m on a straight road with a velocity of 9 km/h. He then continued for the same distance in the same direction, but with a velocity of 6 km/h. Find the magnitude of the average velocity during the whole trip.

Q9:

A car, starting from rest, began moving in a straight line from a fixed point. Its velocity after time 𝑑 seconds is given by ⃑ 𝑣 =  ο€Ή 9 𝑑 βˆ’ 3 𝑑  ⃑ 𝑐  /  m s . Find its average velocity during the time interval between 𝑑 = 0 and 𝑑 = 5 . 5 s .

  • A 1 0 . 4 1 ⃑ 𝑐 m/s
  • B 5 . 5 ⃑ 𝑐 m/s
  • C βˆ’ 1 0 . 4 1 ⃑ 𝑐 m/s
  • D βˆ’ 5 . 5 ⃑ 𝑐 m/s

Q10:

The graph shows the distance, in kilometres, a motorcycle travelled from a certain city to another and back again and the time of the trip, in hours. Find the average speed of the motorcycle on its journey from the first city to the second.

Q11:

A cyclist travelled 10.5 km on a straight road from point 𝐴 towards point 𝐡 at 18 km/h. Then, he turned around from point 𝐡 and headed in the opposite direction and covered 21 km travelling at 28 km/h. Find his average speed 𝑣 and the average velocity ⃑ 𝑣 , expressing it in terms of ⃑ 𝑛 , the unit vector in the direction he started travelling.

  • A 𝑣 = 4 2 / k m h , ⃑ 𝑣 = βˆ’ 6 3 8 ⃑ 𝑛 / k m h
  • B 𝑣 = 1 8 9 8 / k m h , ⃑ 𝑣 = 1 8 9 8 ⃑ 𝑛 / k m h
  • C 𝑣 = 4 2 / k m h , ⃑ 𝑣 = 1 8 9 8 ⃑ 𝑛 / k m h
  • D 𝑣 = 1 8 9 8 / k m h , ⃑ 𝑣 = βˆ’ 6 3 8 ⃑ 𝑛 / k m h

Q12:

Using the displacement-time graph, find the average speed of the body.

  • A 1 0 9 m/s
  • B 5 0 9 m/s
  • C 20 m/s
  • D 7 0 9 m/s
  • E 5 3 m/s

Q13:

A body started moving in a straight line. At time 𝑑 seconds, its velocity is given by 𝑣 = ο€Ή 𝑑 βˆ’ 9 𝑑  / 𝑑 β‰₯ 0 .  m s , Find the body’s average speed during the first 13.5 s of motion.

Q14:

A body moves along a straight line. At time 𝑑 seconds, its velocity is given by 𝑣 = ο€Ή 1 6 𝑑 βˆ’ 1 2 𝑑  / 𝑑 β‰₯ 0 .  m s , Determine the body’s average velocity and its average speed in the time interval 0 ≀ 𝑑 ≀ 3 .

  • Aaverage velocity = 3 8 / m s , average speed = 3 0 / m s
  • Baverage velocity = 1 2 3 4 / m s , average speed = 3 0 / m s
  • Caverage velocity = 3 0 / m s , average speed = 3 8 / m s
  • Daverage velocity = 3 0 / m s , average speed = 1 2 3 4 / m s
  • Eaverage velocity = 1 2 0 / m s , average speed = 1 2 3 / m s

Q15:

A moving particle passed through two points 𝐴 ( 2 , βˆ’ 5 ) and 𝐡 ( 1 , 2 ) at the 6th and 11th seconds, respectively. Find the magnitude of the average velocity of the particle 𝑣 during this period of time and its direction πœƒ to the nearest minute.

  • A 𝑣 = 3 √ 2 5 length units/second, πœƒ = 1 3 5 ∘
  • B 𝑣 = 3 √ 2 length units/second, πœƒ = 3 1 5 ∘
  • C 𝑣 = 5 √ 2 length units/second, πœƒ = 1 3 5 ∘
  • D 𝑣 = √ 2 length units/second, πœƒ = 9 8 8 β€² ∘
  • E 𝑣 = 5 √ 2 length units/second, πœƒ = 9 8 8 β€² ∘

Q16:

The function 𝑠 ( 𝑑 ) = βˆ’ 1 6 𝑑 + 1 4 4 𝑑  gives a projectile’s displacement in meters after 𝑑 minutes. Find the average velocity of the projectile on the interval [ 1 , 2 ] .

Q17:

At the start of a trip, the odometer on a car read 2 1 3 9 5 . At the end of the trip, 13.5 hours later, the odometer read 2 2 1 2 5 . Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip in miles per hour? Give your answer correct to one decimal place.

Q18:

Two bodies started moving from points 𝐴 and 𝐡 in the direction of  𝐡 𝐴 , where the distance between them was 35 km. Given that the bodies were moving with uniform velocities of 1β€Žβ€‰β€Ž400 m/min and 119 km/h, respectively, and that they met at a distance 𝑑 from 𝐴 after 𝑑 minutes, find 𝑑 and 𝑑 .

  • A 𝑑 = 4 9 k m , 𝑑 = 3 5 m i n
  • B 𝑑 = 1 1 9 k m , 𝑑 = 6 0 m i n
  • C 𝑑 = 1 6 8 k m , 𝑑 = 1 2 0 m i n
  • D 𝑑 = 8 4 k m , 𝑑 = 6 0 m i n
  • E 𝑑 = 8 4 k m , 𝑑 = 1 2 0 m i n

Q19:

A diesel ship leaves on a long voyage, heading in a straight line away from shore. When it is 180 miles from shore, a seaplane, whose speed is 10 times that of the ship, is sent to deliver mail, starting from the same departure point as the ship and following the same route. How far from shore does the seaplane catch up with the ship?

Q20:

The given graph describes two straight paths of movement of two cars, 𝐴 and 𝐡 , where the path of 𝐴 is in green and the path of 𝐡 in blue. Both cars move from two different villages, and each car moves from a village heading towards the other. Determine the time taken by car 𝐴 to reach its destination.

  • A 216 min
  • B 144 min
  • C 108 min
  • D 252 min

Q21:

The figure below represents the paths of two cars: car 𝐴 is represented by the green line, and car 𝐡 is represented by the blue one. Car 𝐴 is moving from the capital city to a village, and car 𝐡 is travelling from the village to the capital city. Given that car 𝐡 started moving at 0 1 : 1 8 am, when will it reach the capital city?

  • A 0 5 ∢ 0 2 am
  • B 0 3 ∢ 5 2 am
  • C 0 5 ∢ 5 8 am
  • D 0 2 ∢ 4 2 am

Q22:

The graph represents the paths of two cars 𝐴 and 𝐡 : 𝐴 in green and 𝐡 in blue, where car 𝐴 is moving from village 𝐢 to village 𝐷 , and car 𝐡 from 𝐷 to 𝐢 . How long does it take for the two cars to meet?

Q23:

A cyclist travelled 45.5 km from point 𝐴 to point 𝐡 at 52 km/h, and then he travelled a further 38.5 km in the same direction at 44 km/h. Given that ⃑ 𝑛 is a unit vector in  𝐴 𝐡 direction, determine the cyclist’s average speed 𝑣 and average velocity ⃑ 𝑣 during the whole trip.

  • A 𝑣 = 1 4 7 / k m h , ⃑ 𝑣 = ο€Ή 1 4 7 ⃑ 𝑛  / k m h
  • B 𝑣 = 4 8 / k m h , ⃑ 𝑣 = ο€Ή 4 ⃑ 𝑛  / k m h
  • C 𝑣 = 1 4 7 / k m h , ⃑ 𝑣 = ο€Ή 1 2 . 2 5 ⃑ 𝑛  / k m h
  • D 𝑣 = 4 8 / k m h , ⃑ 𝑣 = ο€Ή 4 8 ⃑ 𝑛  / k m h

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