EQUATION OF MOTION Lesson Note
LEARNING OBJECTIVES: By the end of the class, student should be able to :
This SS2 Physics lesson note covers EQUATION OF MOTION for First Term, Week 3.
Lesson Note
LEARNING OBJECTIVES: By the end of the class, student should be able to :
Define equation of motion
Derive the 4 equations of motion
Solve the problem using he equations
Apply to free fall/ vertical motion
A. DEFINITION:
Equation of motion are equation that describe the relationship between displacement, velocity, acceleration and time for a body moving with uniform acceleration in a straight line.
They are also called kinematic equations.
THE FOUR EQUATION OF MOTION
v = u + at
s = ut + ½at2
s = ½(u + v) t
v2= u2 +2as
DERIAVTIVES:
First equation : v = u + at
From definition of acceleration : a = (v + u)/t
at = v - u
= v = u + at
Second and third equation
Average velocity = ( u + v)/2 but s = average velocity x time
s = ½ (u + v)t………… Equation 3
Put v = u +at into equation 3:
s = ½ (u + u + at)t
s = ½(2u + at)t
s = ut + ½at2
Fourth equation: v2 = u2 +2as
From equation 1: t = (v - u)/a
Put into s = ( u + v)/2 t
s = ( u + v)/2 - ( v - u)/a
s = ( v2 - u2)/2a cross multiply
2as = v2 - u2
v2 = u2 + 2as
Example: A car starts from rest an accelerate at 2 m/s2 for 10s. Find final velocity and distance covered
Solution:
Given u = 0, a = 2. t = 10
v = u + at
v = 0 + 2x10 = 20m/s
Distance covered
s = ut + ½at2
s = 0 + ½x2x100 = 100m
EQUATIONS FOR VERTCAL MOTION (FREE FALL UNDER GRAVITY)
For vertical motion, replace
a = g = acceleration due to gravity (10mls2)
s = h
If a body is thrown upwards, g is negative (-g) because it opposes motion. If falling downwards, g is positive (+g).
Equation become :
v = u ± gt
h = ut ± ½gt2
v2 = u2 ± 2gh
Evaluation
OBJECTIVE QUESTIONS
1. Equations of motion are valid only when acceleration is:
A. Increasing
B. Decreasing
C. Uniform
D. Zero
2. In v = u + at, v represents:
A. Initial velocity
B. Final velocity
C. Distance
D. Time
3. The unit of acceleration is:
A. m/s
B. m/s²
C. m
D. s
4. A body starting from rest means u = ?
A. 1
B. 10
C. 0
D. 100
5. Which equation does NOT contain s?
A. v = u + at
B. s = ut + ½at²
C. v² = u² + 2as
D. s = (u+v)t/2
6. A car accelerates from 10 m/s to 20 m/s in 2s. Acceleration is:
A. 5 m/s²
B. 10 m/s²
C. 15 m/s²
D. 2 m/s²
7. Retardation means acceleration is:
A. Positive
B. Negative
C. Zero
D. Maximum
8. For a body thrown vertically upwards, g is:
A. Positive
B. Negative
C. Zero
D. Same
9. At maximum height of a projectile thrown up, velocity is:
A. Maximum
B. Minimum
C. Zero
D. Equal to u
10. v² = u² + 2as is useful when time (t) is:
A. Given
B. Not given
C. Zero
D. Maximum
THEORY QUESTIONS
1. a) State the four equations of uniform accelerated motion.
b) Derive from first principle: i) v = u + at ii) v² = u² + 2as
c) A car starts from rest and accelerates uniformly at 3 m/s² for 10 seconds. Calculate:
i) Final velocity
ii) Distance covered in that time
2. a) Explain what is meant by retardation with example.
b) A vehicle moving with velocity 20 m/s is brought to rest in 5 seconds by applying brake. Calculate:
i) Retardation
ii) Distance covered before stopping
c) A stone is thrown vertically upwards with velocity 30 m/s. Calculate the maximum height attained. [Take g = 10 m/s²]N: