The displacement (in meters) of a particle moving in a straight line is given by s = t^2 − 7t + 15, where t is measured in seconds.
Find the average velocity over each time interval.
(i)    [4, 5]

The average velocity of a particle over a time interval \([t_1, t_2]\) can be calculated using the formula:

\[
\text{Average velocity} = \frac{s(t_2) - s(t_1)}{t_2 - t_1}
\]

where \(s(t)\) is the displacement function, given as \(s(t) = t^2 - 7t + 15\).

For the interval \([4, 5]\):

1. Find \(s(4)\):
\[
s(4) = 4^2 - 7(4) + 15 = 16 - 28 + 15 = 3
\]

2. Find \(s(5)\):
\[
s(5) = 5^2 - 7(5) + 15 = 25 - 35 + 15 = 5
\]

3. Now, apply the formula for average velocity:
\[
\text{Average velocity} = \frac{s(5) - s(4)}{5 - 4} = \frac{5 - 3}{1} = 2 \, \text{m/s}
\]

So, the average velocity over the interval \([4, 5]\) is \(2 \, \text{m/s}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the average velocity over the interval \([3, 4]\)?
2. How do you find instantaneous velocity using calculus?
3. Can you determine the time when the particle comes to rest?
4. What is the significance of average velocity in motion analysis?
5. How does average velocity differ from instantaneous velocity?

**Tip:** The average velocity gives a general idea of how fast an object is moving over a period, while instantaneous velocity gives the speed at any specific moment.

The displacement (in meters) of a particle moving in a straight line is given by s = t^2 − 7t + 15, where t is measured in seconds. Find the average velocity over each time interval. (i) [4, 5]

Discover how to calculate the average velocity of a particle moving in a straight line over the time interval [4, 5]. Using the displacement function s(t) = t^2 - 7t + 15, this problem demonstrates key kinematic concepts and the formula for average velocity. Suitable for Grades 9-12.

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