Question

Just started learning physics. Need some help understanding the difference between velocity and speed.
question: a car is constrained to move back and forth on a straight track. The car starts at position x=-150m at time t=0. The car moves 290m in a positive direction for 15 seconds at a constant speed. Then the car immediately reverses and travels 240m in the opposite direction for 25 seconds at a constant (but different) speed. What is the car's average velocity? Average speed?

Answer 1

This is an idea that confuses many new students. Speed is what is called a vector quantity, meaning it has two parts, (1) magnitude and (2) direction. Direction is a scaler quantity meaning it only has (1) magnitude.
Imagine we are running around a track. Although we maintain the same speed, our velocity changes because we are changing direction in each of the four corners.

Now onto your particular problem. The starting position and starting time are not important here. So first we travel +290m in 15 seconds. We know that velocity is defined as:\[v = {\rm distance \over time} = {d \over t}\]Therefore, we can find that the velocity is\[v_1 = {290 \over 15}\]
The second move is -240m in 25 seconds. Therefore, the velocity here is: \[v_2 = {-240 \over 25}\]

The average velocity will be \[v_{avg} = {v_1 + v_2 \over 2}\]The average speed will be\[{\rm speed}_{avg} = { |v_1| + |v_2| \over 2 }\]

Answer 2

thank you :). Very easy to understand too.