# What is the average velocity vav of the particle over the time interval δt=50.0s ?

1/What is the total distance Delta x traveled by the particle?
2/What is the average velocity Vav of the particle over the time interval Delta t= 50.0 s ?
3/
What is the instantaneous velocity v of the particle at t=10.0s ?

## General guidance

Concepts and reason
The concept used to solve this problem is the fundamental equations of the kinematics. Initially, the total distance can be calculated by subtracting the initial position from the final position. Later the average velocity can be calculated from the slope of the given graph. Finally, the instantaneous velocity of the particle will be the average velocity of the particle as the particle is moving with constant velocity.

Fundamentals

The total distance travelled by the particle is, Here, is the total distance travelled by the particle, is the final position of the particle and is the initial position of the particle. The average velocity of the particle is, Here, is the average velocity, and is the time taken by the particle.

## Step-by-step

### Step 1 of 3

(1) The expression for the travelled distance is, Substitute forand for

Part 1

The travelled distance by the particle is.

The travelled distance by the particle is calculated by subtracting the initial position from the final position.

### Step 2 of 3

(2) The expression for the average velocity is, Substitute for, 50s for

Part 2

The average velocity for the particle is.

The average velocity of the particle is calculated by substituting the total distance and time in the kinematics equation.

### Step 3 of 3

(3) The expression for the instantaneous velocity is, Substitute for.

Part 3

The instantaneous velocity of the particle is

The instantaneous velocity of the particle is equal to the average velocity as the particle is moving with a constant velocity.