Acceleration is defined as:
a = (change in velocity) / time
a = v − ut
Multiplying both sides by t:
at = v − u
Adding u to both sides:
u + at = v
Therefore:
v = u + at
9. Meaning of the First Equation
The change in velocity during time t is:
Δv = at
Therefore:
Final velocity = Initial velocity + Change in velocity
v = u + at
If acceleration is negative, velocity decreases with time.
10. Solved Example 1: Finding Final Velocity
Solved Example 1: Finding Final Velocity
A car has an initial velocity of 10 m s⁻¹. It accelerates uniformly at 2 m s⁻² for 5 s. Find its final velocity.
1
Given
u = 10 m s⁻¹
a = 2 m s⁻²
t = 5 s
Required: v = ?
Formula: v = u + at
2
Working
v = 10 + (2)(5)
3
Step 2
v = 10 + 10
4
Step 3
v = 20 m s⁻¹
Final answer:v = 20 m s⁻¹
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Explanation after each answer
Practice
Practice
Q1. A car starts from rest and accelerates at 4 m s⁻² for 6 s. Find its final velocity.
Practice
Q2. An object is dropped for 4 s. Find its final velocity using g = 10 m s⁻².
Practice
Q3. An object falls from rest through 80 m. Find its time and final velocity using g = 10 m s⁻².
