Question

speed & velocity
you will be given the formula for velocity: $v = \frac{\delta x}{\delta t}=\frac{x_f - x_i}{t_f - t_i}$
no need to memorize it!
question
write the formula for velocity in words.
what is the difference between speed and velocity?
what is the difference between instantaneous velocity and average velocity?
problem 1:
an olympic swimmer swims 50 m in 23.1 secs. what is his average velocity?

Explanation:

Step1: Define velocity formula in words

Velocity is the change in position ($\Delta x=x_f - x_i$, where $x_f$ is final position and $x_i$ is initial position) divided by the change in time ($\Delta t=t_f - t_i$, where $t_f$ is final time and $t_i$ is initial time).

Step2: Differentiate speed and velocity

Speed is a scalar quantity, only has magnitude. Velocity is a vector quantity, has both magnitude and direction.

Step3: Differentiate instantaneous and average velocity

Instantaneous velocity is the velocity at a specific instant in time. Average velocity is the total displacement ($\Delta x$) divided by the total time interval ($\Delta t$) over a period of time.

Step4: Solve for average velocity in problem 1

Use the formula $v=\frac{\Delta x}{\Delta t}$. Here, $\Delta x = 50m$ and $\Delta t=23.1s$. So $v=\frac{50}{23.1}\approx2.16m/s$.

Answer:

• Write the formula for velocity in words: Velocity is the change in position divided by the change in time.
• What is the difference between speed and velocity? Speed is scalar, velocity is vector.
• What is the difference between instantaneous velocity and average velocity? Instantaneous is at a point, average is over a time - interval.
• Problem 1: His average velocity is approximately $2.16m/s$.