AVERAGE VELOCITY WORKSHEET

Problem 1 :

An object moves along a straight line so that its position in meters is given by s(t) = t³ - 6t² + 9t for all time in t seconds. Find the average velocity of the object between t = 2 and t = 5 seconds.

Problem 2 :

The position of a car is given by s = 10 + 5t + 20t² meters at t seconds. What is the average velocity between t = 0 and t = 10 seconds?

Problem 3 :

An object is dropped from the observation deck of the CN tower so that its height in meters is given by

h(t) = 447 - 4:9t²

where t is measured in seconds (we are neglecting air resistance). What is the average velocity between t = 1 and t = 2 seconds?

Problem 4 :

A car travels along a straight road to the east for 120 meters in 4 seconds, then go to the west for 40 meters in 1 second. Determine average velocity.

Problem 5 :

A car travels along a straight road to the east for 40 meters in 1 second, then go to the west for 150 meters in 4 seconds. Determine average velocity.

Problem 6 :

A truck driver drives 20 km down the road in 5 minutes. He then reverses and drives 12 km back down the road in 3 minutes. What is his average velocity?

Problem 7 :

A runner is running around rectangle track with length = 50 meters and width = 20 meters. He travels around rectangle track twice, finally running back to starting point. If the total time he takes to run around the track is 100 seconds, determine average speed and average velocity.

Problem 8 :

A man starts walking from a point on a circular field of radius 0.5 km and 1 hour later he finds himself at the same point where he initially started.

Problem 9 :

What is the average speed of my bunny rabbit when she hops 6 meters to the east across the room in 11 seconds? Express your answer using the proper SI units. Round your answer to two decimal places, and include a direction if necessary.

Problem 10 :

How many minutes does Ziko take to cover a distance of 400 m, if he runs at a speed of 20 km/hr ?

1. Answer :

The average velocity between t = 2 and t = 5 is given by

=  [s(5) - s(2)] / (5 - 2)

=  [s(5) - s(2)] / 3

s(5) = 5³ - 6(5)² + 9(5) = 20

s(2) = 2³ - 6(2)² + 9(2) = 2

=  (20 - 2)/3

=  18/3

=  6 m/s

2. Answer :

The average velocity between t = 0 and t = 10 is given by

=  [s(10) - s(0)] / (10 - 0)

=  [s(10) - s(0)] / 10

s(10) = 10 + 5(10) + 20(10)² = 2060

s(0) = 10 + 5(0) + 20(0)² = 10

=  (2060 - 10)/10

=  2050/10

=  205 m/s

3. Answer :

The average velocity between t = 1 and t = 2 is given by

=  [h(2) - h(1)] / (2 - 1)

=  [h(2) - h(1)] / 1

=  h(2) - h(1)

h(2) = 447 - 4:9(2)² = 427.4

h(1) = 447 - 4:9(1)² = 442.7

=  427.4 - 442.7

=  -15.3

=  -15.3 m/s

4. Answer :

Average Velocity :

=  Displacement / Time elapsed

=  (120 - 40)/(4 + 1)

=  80/5

=  16 m/s

5. Answer :

Average Velocity :

=  Displacement / Time elapsed

=  (150 - 40)/(1 + 4)

=  110/5

=  22 m/s

6. Answer :

Average Velocity :

=  Displacement / Time elapsed

=  (20 - 12)/(5 + 3)

=  8/8

=  1 km/min

7. Answer :

The perimeter of the rectangle is the distance travelled in one round. That is

=  2(50 m) + 2(20 m)

=  100 m + 40 m

=  140 meters

Runner runs around the rectangle twice and the distance covered :

=  2(140 m)

=  280 meters

He has completed two rounds around the rectangle and now he is at the starting point. 

Then the displacement = 0 meters. 

Average Velocity :

=  Displacement / Time elapsed

=  0/100

=  0 m/s

8. Answer :

If the man walks around in a circle and comes back to the same point where he started in a circle, then the change in his position is zero and the displacement is also zero. 

Average Velocity :

=  Displacement / Time elapsed

=  0/1

=  0 km/hr

9. Answer :

Distance covered = 6 m

Time taken = 11 seconds

Average speed = Total distance covered / total time taken

= 6/11

= 0.545 

Approximately 0.55 m/seconds.

10. Answer :

Average speed of Ziko = 20 km/hr

Converting km/hr to m/seconds

1 km = 1000 m

1 hour = 60 seconds

20 km/hr = 20 x (1000/60x60)

= 20 x (5/18)

= 50/9 m/sec

Time taken to cover 400 m = Distance / speed

= 400 / (50/9)

= 400 x (9/50)

= 72 seconds

Converting seconds into minutes :

1 hour = 60 minutes

1 minute = 60 seconds

72 seconds = 72/60

= 1.2 minutes

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