1. Punctuality

a. The last person to come into the class later than me will teach the class for 10 minutes

b. Homework to be returned during the first Theory lesson of the week.

2. Cleanliness

3. Courtesya. If you need to speak, raise your hands.

4. Consistencya. You must always have your notes with you.

Class Rules

Kinematics Part 5

Equations of Motion

Learning O

bjectives

By the end of the lesso

n, you should be able to:

i)Interpret given examples o

f non-uniform

acceleration.

ii)Solve problems u

sing equations w

hich

represent uniformly accelerated motion in

a straight lin

e, including the motion of

bodies fallin

g in a uniform gravitational

field without air resist

ance.

Galileo Galilei and His ExperimentsPredict-Observe-Explain

Recall in the earlier lesson, we have learnt to determine the physical quantities associated with motion graphically.

In this lesson, we shall learn how to calculate from the Equations of Motion.

Personally, I like to call them, the Equations of Uniform Acceleration because these equations are

ONLY APPLICABLE UNDER UNIFORM ACCELERATION!

The Equations of Motion

The Equations of Motion

asuv

atuts

tvus

atuv

222

22

1

2

1

sauv

tauts

tvus

tauv

222

22

1

2

1

Where s = Δs, that is the change in displacement;

t = Δt, that is, the change in time or the time taken;

u = initial velocity;

v = final velocity;

a = acceleration

The four equations of motion is given on the left.

Each equation caters to finding an unknown physical quantity if three other are known.

However, they are often written in the following form, omitting “Δ”.

1

2

3

4

12 tt

uva

Deriving the Equations of Motion

The first equation of motion was derived from the definition of acceleration, given the situation when acceleration is UNIFORM.

Time/s

Velo

city

/ m

s-1

v

t

(t1, u)

(t2, v)

t1 t2

u

v

Equation 1. v = u + at

t

uva

uvta

tauv

The 2nd equation of motion was derived from determining displacement under the v(t) graph, given the situation when acceleration is UNIFORM.

Time/s

Velo

city

/ m

s-1

Deriving the Equations of Motion

t

(t1, u)

(t2, v)

t1 t2

u

v

tvus 2

1

Equation 2. tvus 2

1

Displacement, s = area under graph

= area of trapezium

= ½ X (sum of // sides) X ht.

= ½ X (u + v) X Δt

• Armed with Equation 1 and 2, we may derive Equation 3 and 4.

• Can you try deriving Equation 3 and 4?

• Are you able to derive a 5th equation of uniform acceleration? What variables will it contain?

Deriving the Equations of Motion

Equation 3 and 4. &2

2

1 atuts asuv 222

Using the Equations of Motion

1. Optimus Prime accelerates at a rate of 0ms-2 from an initial velocity of 2ms-1 for 10s. What is its velocity at the end of 10s?

2. Meanwhile, Bumblebee accelerates from rest to 10ms-1 in 5s. What is its displacement by the end of the 5s?

3. Megatron tore through the atmosphere at a constant velocity of 400kmh-1 for 5s and then accelerates at 10kmh-2 in the next 3s. What is his displacement during the entire 8s?

4. Starscream tore through the atmosphere at a constant velocity of 400kmh-1 for 10s. What is his acceleration during this 10s?

Simple Examples – Direct Application of Equations

Using the Equations of Motion

5. A ball drops from the top of a building. If the ball takes 4s to impact the ground below, what is the final velocity of the ball before it hits the ground?

6. A ball drops from the top of a building. If the ball took 4s to impact the ground below, what is the height of the building?

7. A ball drops from the top of a building with an initial velocity of 5ms-1. If the ball took 4s to impact the ground below, what is the height of the building?

8. What is the final velocity of the ball from (c), just before impact, if a 1.5m tall (or short) man was standing just below the ball? (Taking acceleration due to gravity, g = 10ms-2)

9. Whose fault is it if the man should get injured (or loses his head)?

Simple Examples – Direct Application of Equations

Using the Equations of Motion

1. A lunar landing module is descending to the Moon’s surface at a steady velocity of 10ms-1. At a height of 120m, a small object falls from its landing gear. Taking the Moon’s gravitational acceleration as 1.6 ms-1, at what velocity does the object strike the Moon?

2. The velocity of a car which is decelerating uniformly changes from 30ms-1 to 15ms-1 in 75m. After what distance will it come to rest?

Slightly More Advance Situations