Distance

Distance is defined as the difference between two points. It is a scaler quantity.

It is also the sum of all length moved by an object.

The unit of distance is in meter(m).

Other units are the mm,cm,km and so on. But the S.I units is in meter (m).

Example

Find the distance moved by a monkey moving from point A to B back to A. If the distance between A and B is 3m

A____________3m__________B

Recall that distance is the sum of all length thus ..

A to B=3m

Back to A again=3m

Total distance =3+3=6m

In addition, distance is not specified by the moving body.

Don't worry, when you get to displacement. You will understand better

Speed

Speed is the rate of change of distance. So we can say for simplicity, speed is how fast you can move a distance. Since distance is a scaler, and speed is the rate if change of distance. Then we can say speed is a scaler quantity.

The formula for calculating speed is given by the relationship

Speed =distance/time

Example

A railway moves along a distance of 5m. Calculate the speed of the of the railway in 4secs.

Solution

distance=5m,

Time=4secs.

Recall that speed is distance/time

Speed=5/4=1.25m/s.

Example 2

A car runs a distance of 5m in a unknown seconds. Find the time taken if the speed is 3m/s

Solution

Speed=3m/s, t=?, distance=5m

Speed=distance/time

3=5/t

Cross multiply,we have

3t=5

t=5/3=1.67secs.

Example 3

What is the distance moved by light in 4secs (take the speed of light as 3x10^9).

Solution

Speed=distance/time

Speed from the question is 3x10^9m/s

distance=?, Time =5secs

From the formula

Then

3x10^9=distance/5

Cross multiply

3x10^9x5=distance

distance=15x10^9m or 15x10^6km

Let's pulse here for now

DISPLACEMENT

If I say "I am going to 5m directly north", am going to that church 5m away from my house". I am specifying my distance.

So displacement is the distance moved in a specified direction. Now understand the fact that distance is not specified. The unit of displacement is thesame as that of distance. It is measured in meter( m)

Displacement is a vector quantity. But distance is a scaler.

In a question how do u know if it's distance or displacement? Very simple. If it's distance its direction will not be specified.

Example

Classify the following as distance or displacement

(a)A man moved 4m, 30° north (b) a cow ran 45m

(c)A projectile fired 45° to the horizontal (d) a car moved a distance of 3km

Answers

a. Is displacement

b. Is distance

C. displacement

D. Distance...

*It's not the sum of all length moved

Example

A body moved from A to B, and back to A. Find the displacement of the particle

A________3m______B

Solution

Since, it's the distance moved in a specified direction, the only specified direction above is from A to B., Which is 3m.

No other Futher specific distance moved.

So the displacement is 3m.

Velocity

Velocity is the time rate of change in displacement.

It is how fast displacement take place.

If v is velocity and S is displacement, where t is the time taken , then

velocity=displacement/time or in short form v=s/t.

Velocity is a vector quantity. The unit is in meter per seconds (m/s or ms—¹)

Example

A truck ran with a certain velocity. Moving a distance of 54m towards a taxi car in 90secs. Find the velocity of the truck.

Solution

v=?

s=54m

t=90secs

Recall

v=s/t

v=54/90

Example 2

Find the displacement an object travelled in 60secs with a velocity of 60m/s.

Solution

s=?

t=60secs

v=60m/s

From v=s/t

i.e 60=s/60

s=60 x 60 =3600m

Very easy!!

Exercise from so far topics

(1) Find the distance moved by an aircraft in 5minutes. If it's speed is 9m/s

(2) if v=6m/s find s when t=5mins

(3) make t the subject of the formula

v= s/t

ACCELERATION

we often hear the word acceleration, but in some cases we don't really know the meaning. Asumming am on my car driving to Benin. On my way I heard a pho e call that I have few minutes to be there, immediately I heard that I increased the speed of my car very faster than it was before. What I have just done is called acceleration.

Acceleration: is the rate of change in velocity. Or the change in velocity with respect to time. For simpler understanding, in linear motion. It's the "increase in speed"

We say

a=v/t

Where a= acceleration

v=velocity

And t= time

# Exam Success Point

## Wednesday, March 27, 2019

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