5.1 How Do We Measure Distance Travelled

Question 1

What is the key question addressed in section 5.1?

Answer 1

How do we measure the total distance traveled by an object over a period of time when its speed varies?

Question 2

What basic mathematical concept is introduced to measure distance travelled?

Answer 2

The concept of integration is introduced to sum up small distances over time.

Question 3

How is the distance traveled by an object related to its velocity?

Answer 3

Distance travelled is the integral of the velocity function with respect to time.

Question 4

What does the velocity function v(t) represent?

Answer 4

the speed of the object at any given time t

Question 5

What is the formula for distance travelled if the velocity is a function of time v(t)?

Answer 5

The distance traveled is given by
∫ (b on top and a on the bottom)
​v(t)dt, where t ranges from a to b.

Question 6

What does the integral ∫ (b on top and a on the bottom) v(t)dt geometrically represent?

Answer 6

It represents the area under the curve of the velocity function v(t) from t=a to t=b.

Question 7

What is the meaning of a positive versus negative value of v(t) in terms of distance?

Answer 7

A positive v(t) means the object is moving forward, while a negative
v(t) means the object is moving backward.

Question 7

What is the total distance travelled if the object changes direction during the time interval?

Answer 7

the integral of the absolute value of the velocity function: ∫ (b on top and a on the bottom) v(t)∣dt.