The table shows the position of a cyclist.

t (seconds) 0 1 2 3 4 5
s (meters) 0 1.6 4.6 10.4 17.8 25.2

(a) Find the average velocity for the time period [1, 3].
? m/s

(b) Find the average velocity for the time period [2, 3].
? m/s

(c) Find the average velocity for the time period [3, 5].
? m/s

(d) Find the average velocity for the time period [3, 4].
? m/s

Help! I have no idea where to start with this question!

Do them all the same way.

It would e easier to see if the numbers in your table lined up one above the other.
The average velocity between time 1 (t1) and time 2 (t2) is:
(position2 - position1)/(t2 - t1)

The first answer is
(10.4 - 1.6)/(3 -1) = 3.25 m/s

Thank you! I was trying to make it harder than it really was! lol! Thank you again!

how do i find the instaneous velocity at t=

3

To find the average velocity for a given time period, you need to calculate the change in position and divide it by the change in time. Here's how you can solve each part of the question:

(a) To find the average velocity for the time period [1, 3], you need to calculate the change in position and divide it by the change in time. The change in position is the final position minus the initial position, and the change in time is the final time minus the initial time. In this case, the initial time is 1 second, and the final time is 3 seconds. The initial position is given as 1.6 meters, and the final position is given as 10.4 meters.

So, the change in position is 10.4 - 1.6 = 8.8 meters, and the change in time is 3 - 1 = 2 seconds.

Now, divide the change in position by the change in time to find the average velocity: 8.8 meters / 2 seconds = 4.4 m/s.

Therefore, the average velocity for the time period [1, 3] is 4.4 m/s.

(b) To find the average velocity for the time period [2, 3], you follow the same steps as in part (a). The initial time is 2 seconds, and the final time is 3 seconds. The initial position is given as 4.6 meters, and the final position is given as 10.4 meters.

Calculate the change in position: 10.4 - 4.6 = 5.8 meters. The change in time is 3 - 2 = 1 second.

Divide the change in position by the change in time: 5.8 meters / 1 second = 5.8 m/s.

Therefore, the average velocity for the time period [2, 3] is 5.8 m/s.

(c) Repeat the same steps for the time period [3, 5]. The initial time is 3 seconds, and the final time is 5 seconds. The initial position is given as 10.4 meters, and the final position is given as 25.2 meters.

Calculate the change in position: 25.2 - 10.4 = 14.8 meters. The change in time is 5 - 3 = 2 seconds.

Divide the change in position by the change in time: 14.8 meters / 2 seconds = 7.4 m/s.

Therefore, the average velocity for the time period [3, 5] is 7.4 m/s.

(d) Finally, the last part is to find the average velocity for the time period [3, 4]. The initial time is 3 seconds, and the final time is 4 seconds. The initial position is given as 10.4 meters, and the final position is given as 17.8 meters.

Calculate the change in position: 17.8 - 10.4 = 7.4 meters. The change in time is 4 - 3 = 1 second.

Divide the change in position by the change in time: 7.4 meters / 1 second = 7.4 m/s.

Therefore, the average velocity for the time period [3, 4] is 7.4 m/s.

I hope this explanation helps you understand how to solve each part of the question!