Question

check for understanding:

1. compare and contrast speed and velocity. how are they the same? how are they different?

speed and velocity are the same because...
speed and velocity are different because...

1. what is the speed of a car that travels 7 meters in 40 seconds?

Explanation:

Step1: Recall the definitions

Speed is a scalar quantity that measures how fast an object is moving. The formula for speed is \(s=\frac{d}{t}\), where \(d\) is distance and \(t\) is time. Velocity is a vector quantity. It measures the rate at which an object changes its position (so it has both magnitude and direction). The formula for velocity is \(v = \frac{\Delta x}{\Delta t}\), where \(\Delta x\) is displacement (a vector quantity representing the change in position) and \(\Delta t\) is time.

Step2: Analyze the similarities

Both speed and velocity are measures related to the motion of an object. They both use the formula of a quantity related to the change of a position - like measure (distance for speed, displacement for velocity) divided by time. Mathematically, if an object is moving in a straight - line without changing direction, the magnitude of its speed and velocity (when we just consider the magnitude of the velocity vector) can be calculated using similar arithmetic (dividing a length - like quantity by time).

Step3: Analyze the differences

Speed is scalar. For example, if a car goes around a circular track and comes back to its starting point, the average speed is the total distance around the track divided by the time taken. Velocity is vector. In the same circular - track example, since the displacement (final position - initial position) is zero (because the car ends up where it started), the average velocity is zero.

Step4: Calculate the speed for the second question

Given \(d = 7\space m\) and \(t=40\space s\). Using the formula \(s=\frac{d}{t}\), we substitute the values: \(s=\frac{7}{40}=0.175\space m/s\)

Answer:

• Speed and velocity are the same because they both describe how an object's position changes over time (using a formula with a length - like quantity divided by time).
• Speed and velocity are different because speed is a scalar (only has magnitude) and velocity is a vector (has magnitude and direction).
• The speed of the car is \(0.175\space m/s\)