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Average velocity
and average speed

Exercises -solutions

A turtle with a red paint brush attached to its shell is placed on a grid. The turtle is allowed to crawl around the grid at random and traces out the path shown on the left. Each square is 10m X 10m.
a) Calculate the total distance covered by the turtle.
Solution
b) Calculate the displacement of the turtle.
The turtle finishes 50 East of the start.
The turtle takes 40 minutes to complete its journey
c) Calculate the average speed of the turtle.
average speed = total distance / Δt = 356m / (40 X 60) = 0.15m/s

d) Calculate the average velocity of the turtle.
0.15m/s East

An ant crawls around a pathway in search of food. Its movement is traced out on the image on the left.
a) Calculate the total distance covered by the ant.
300 m
b) Calculate the displacement of the ant.

30 m
The ant takes 30 minutes to complete its journey
c) Calculate the average speed of the ant.
300 m / (30 X 60) = 0.17 m/s
d) Calculate the average velocity of the ant.
0,17 m/s South

A hiker sets out on the course shown on the right. It takes her 3 hours to complete her journey.

a) Calculate the average speed of the hiker.
Total distance covered 100 km
=> 100 km / 3hr = 33.3km/hr

b) Calculate the average velocity of the hiker.
Displacement 72 km
=> 72 km / 3hr = 24km/hr North - East

A hiker sets out on the course shown on the right. It takes her 3 hours to complete her journey.

a) Calculate the average speed of the hiker.
Total distance covered 190 km
=> 190 km / 3hr = 63.3km/hr
b) Calculate the average velocity of the hiker.
Displacment 139 km
=> 139 km / 3hr = 46.3km/hr North - East

 

A turtle with a red paint brush attached to its shell is placed on a grid. The turtle is allowed to crawl around the grid at random and traces out the path shown on the left. Each square is 10m X 10m.
a) Calculate the total distance covered by the turtle.
Total distance covered 400 m
b) Calculate the displacement of the turtle.

Displacment = 0
The turtle takes 60 minutes to complete its journey
c) Calculate the average speed of the turtle.
Total distance covered 400 m
=> 400m/(60X 60) = 400/3600 = 0.11 m/s
d) Calculate the average velocity of the turtle.


velocity = 0.
A ball circles inside a cylinder of radius 12m as shown in the animation on the left.

a) Calculate the total distance the ball travels
Total distance covered 2 X 3.142 X 12m = 75.4m
b) Calculate the displacement of the ball.
0


The ball takes 30 minutes to complete one revolution
c) Calculate the average speed of the ball.
Total distance covered 75.4m
=> 75.4m / (30 X 60)= 0.042m/s
d) Calculate the average velocity of the ball.

  0
A car leaves home, travelling due north, at 6.30 am and arrives at a motel 230km away at 8.50 am on the same day.
a) What is its average speed?
Total distance covered 230 km, total time is 110 minutes (1.83 hours)
=> 230 km / 1.83 hr = 126 km/hr

b) What is its average velocity? 126 km/hr North

A motorbike rider heads West on a straight road for what should be a 300km trip. She goes 110km in 50 minutes and then realises she has dropped her hand bag. She backtracks 50km in 20 minutes, finds the wallet and continues on her way. It takes her 2 hours to complete her journey.
a) What is the distance covered by the rider? 400 km
b) What is the displacement of the rider at the end? 300 km West
c) What is her average speed of the rider?400 km/ 2hr = 200 km/hr
d) What is her average velocity? 300 km/ 2hr = 150km/hr West

 

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