Table 2 shows the velocity of an object at different times.

Time(s)| Velocity(cm/s east)
0 | 0
5 | 7.8
15 | 24.3
20 | 31.8
35 | 57.3
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K they have given me the velocity for 5 s, 15, etc. but I want to know the velocity for the other numbers like 2s 4s, etc. How do I figure that out?

To find the velocity at times that are not explicitly given in the table (such as 2s or 4s), you can use interpolation. Interpolation allows you to estimate values between known data points.

In this case, you have two known data points that are closest to the desired time. For example, to find the velocity at 2s, the closest known points are 0s (with a velocity of 0 cm/s) and 5s (with a velocity of 7.8 cm/s).

You can use the following formula to interpolate:

Velocity at desired time = Velocity at time 1 + (Desired time - Time 1) / (Time 2 - Time 1) * (Velocity at time 2 - Velocity at time 1)

Substituting the values:

Velocity at 2s = 0 cm/s + (2s - 0s) / (5s - 0s) * (7.8 cm/s - 0 cm/s)

Velocity at 2s = 2/5 * 7.8 cm/s

Velocity at 2s ≈ 3.12 cm/s

Similarly, you can use this interpolation formula to find the velocity at other desired times such as 4s or any other value between the known data points.

To figure out the velocity for the times between the given values, you can use interpolation. Interpolation is a method used to estimate values between two known data points.

In this case, we have the velocity at times 5s and 15s. Let's say we want to find the velocity at 2s. To do this, we can use linear interpolation.

Here's how you can calculate it:

1. Determine the time interval between the two given times: 15s - 5s = 10s.

2. Calculate the velocity difference between the two times: Velocity at 15s - Velocity at 5s = 24.3 cm/s - 7.8 cm/s = 16.5 cm/s.

3. Divide the velocity difference by the time interval: Velocity difference / Time interval = 16.5 cm/s / 10s = 1.65 cm/s per second.

4. Multiply the velocity per second by the time difference between the desired time and the starting time: Velocity per second * Time difference = 1.65 cm/s * (2s - 5s) = 1.65 cm/s * (-3s) = -4.95 cm/s.

5. Finally, subtract or add the result from your starting velocity: Velocity at 5s + Interpolated velocity = 7.8 cm/s + (-4.95 cm/s) = 2.85 cm/s.

To find the velocity at other times, follow the same process. Calculate the time interval, divide the velocity difference by the time interval, and multiply it by the time difference between the desired time and the starting time.

By using this method of linear interpolation, you can estimate the velocities at the desired times.