# Basics

Linear Motion

What does Linear mean? What does Motion mean?

All the problems in this section will be dealing with the motion of bodies in a straight line

Something is moving if the distance of the body from a point is changing with time.

Displacement is similar to distance from a point, however displacement is a vector and to that end it must have a direction incorporated into its value.

This could be done by saying we are 300m in a N30oE direction, or expressed in i & j values, such as 30i - 40j these are both vector quantities.

So what are we talking about. What moves in a straight line?

What doesn't move in a straight line ?

If a curved line is so uncurved can it be considered straight?

A cruise ship goes across the ocean on what is seemingly a very flat place ?

To start off what measurements can we take along a straight line?

How can you describe motion of a car ?

It is ______ or _______ ?

What makes something ______ or _______ ?

fast or slow, what is fast or slow a measure of ??Time!!!

So now we have Distance and Time .... how do we judge the fastness of a body

okay it took the 1st Miner 30 mins to get out of the mine a distance of 679m calculate the speed of the phoenix 2

but the last miners cart took 11 minutes from the bottom to the top calculate the average speed of the 2 journeys

Velocity is the rate of change of distance with respect to time, in a given direction

Acceleration is given by

there are 5 values that we need to work from

u initial velocity

v final velocity

a acceleration

s displacement

t time

we need to work from these 5 values everytime ...... so write out the letters and any values you know

note that time is the only not vector value here (scalar)

the derivations can be found here

These equations will be in the book of equations you are entitled to in the exam, but you should have enough experience with these equations that they are recalled without but difficulty.

Leaving cert physics students have to be able to derive these equations

As Mr O Murphy takes these equations alongside the graphs of motion we better do some questions

1. From rest with an acceleration of 0.5m/s2 how many seconds would it take to get to 14m/s ?
2. 0 to 22.5 m/s in 4.5s what acceleration does this require ?
3. if something falls from rest for 3 seconds how far does it fall ?
4. 32m/s to rest in 90m what acceleration are we needing ?

Find the missing value ... EDIT / REVISE

1. u=0m s−1, a=4m s−2, t = 6 s, s = ?

2. u=5m s−1,a=3m s−2,t = 3 s, v = ?

3. u=0m s−1,a=4m s−2,t = 4 s, s = ?

4. u=7m s−1,v=15 m s−1,t = 10 s, s = ?

5. u=4m s−1,v=10 m s−1,s = 7m, a = ?

6. v=30 m s−1,a=6 m s−2,t = 2s, u = ?

7. u=6m s−1,v=3m s−1,s = 1.5 m, a = ?

8. s=35 m,a=6 m s−2,t=2 s,u=?

9. s=40 m,u=5 m s−1,v=15 m s−1,t=?

10.u=5m s−1,v=10 m s−1,a = 0.5 m s−2 , s = ?

11.u=48 m s−1,v=12 m s−1,t = 9 s, a = ?

12.s=30m,t=2s,a=4m s−2,v=?

13.s=120m,t=3s,v = 10m s−1,a =?

14.s= −4m,a=2m s−2,v=3m s−1,t= ?

15.s=8m,v=7m s−1,a=3m s−2,t=?

16.s=24 m,u=5 m s−1,a= 2 m s−2,t= ?

17.s=8m,u=6m s−1,a=−2m s−2,t=?

18.v=72 km h−1,a=0.5 m s−2,t = 1min,u =?

these questions were taken from http://www.studentxpress.ie/Applied%20Maths/UAM%20Exercise%201.pdf

Calculate the velocity and acceleration in the following applets

http://vnatsci.ltu.edu/s_schneider/physlets/main/constvel1.shtml

http://vnatsci.ltu.edu/s_schneider/physlets/main/constaccel1d.shtml