Units for velocity, acceleration, and time in kinematic equation 1

📚 Units for Velocity

Velocity is the measure of how quickly an object changes its position. It's a vector quantity, meaning it has both magnitude (speed) and direction.

• 📏 SI Unit: The standard unit for velocity in the International System of Units (SI) is meters per second, represented as $m/s$ or $m \cdot s^{-1}$.
• 🚗 Everyday Examples: When you're driving, your speedometer usually displays your speed in kilometers per hour ($km/h$) or miles per hour ($mph$), but in physics, we convert these to $m/s$ for calculations.
• 🧮 Conversion: To convert $km/h$ to $m/s$, multiply by $\frac{5}{18}$. To convert $mph$ to $m/s$, multiply by $0.44704$.

📚 Units for Acceleration

Acceleration is the rate at which an object's velocity changes over time. Like velocity, it is also a vector quantity.

• ⏱️ SI Unit: The SI unit for acceleration is meters per second squared, represented as $m/s^2$ or $m \cdot s^{-2}$.
• 🎢 Understanding: An acceleration of $5 \frac{m}{s^2}$ means that the velocity of an object increases by $5 \frac{m}{s}$ every second.
• 🍎 Real-world: Consider a car accelerating from 0 to 60 mph in 10 seconds. This involves converting mph to m/s and then calculating the acceleration.

📚 Units for Time

Time is a fundamental quantity that measures the duration of events and the intervals between them.

• ⏳ SI Unit: The SI unit for time is the second, denoted as $s$.
• 📅 Other Units: While seconds are standard, time can also be measured in minutes (min), hours (h), days, years, etc. However, for physics calculations, it's almost always converted to seconds.
• ⏱️ Importance: Accurate measurement of time is crucial in physics, especially when analyzing motion and calculating velocity and acceleration.

📚 Kinematic Equation 1

Kinematic Equation 1 relates final velocity ($v$), initial velocity ($v_0$), acceleration ($a$), and time ($t$):

$v = v_0 + at$

• 🚀 Final Velocity ($v$): Measured in $m/s$.
• 🏁 Initial Velocity ($v_0$): Measured in $m/s$.
• 🎢 Acceleration ($a$): Measured in $m/s^2$.
• ⏱️ Time ($t$): Measured in $s$.

📚 Examples

Let's look at some examples using the kinematic equation and these units:

1. Example 1:

   A car starts from rest ($v_0 = 0 \frac{m}{s}$) and accelerates at a constant rate of $3 \frac{m}{s^2}$ for $5$ seconds. What is its final velocity?

   Using the equation: $v = v_0 + at = 0 + (3 \frac{m}{s^2})(5 s) = 15 \frac{m}{s}$

2. Example 2:

   A ball is thrown upwards with an initial velocity of $20 \frac{m}{s}$ and experiences an acceleration due to gravity of $-9.8 \frac{m}{s^2}$. What is its velocity after $2$ seconds?

   Using the equation: $v = v_0 + at = 20 \frac{m}{s} + (-9.8 \frac{m}{s^2})(2 s) = 0.4 \frac{m}{s}$

📚 Table of Units

Here's a handy table summarizing the units: