### Problem 1.**(Free fall)** The position function of the object is given by:\[ s(t) = s_0 + v_0 t - \frac{1}{2} gt^2 \]where:- \( s_0 \) is the initial position in meters from the ground level,- \( v_0 \) is the initial velocity,- Use \( g \approx 9.8 \, \text{m/s}^2 \),- \( t \) is the time measured in seconds after the object is dropped.*Find the velocity of an object that is released with 0 initial velocity from a height of 300 m at the moment it hits the ground. Round your answer to the nearest hundredth m/s.*### Problem 2.Find the instantaneous rate of change.1. *Find the rate of change of the area of a square with respect to its side \( s \) when \( s = 5 \).*2. *Find the rate of change of the diameter of a circle with respect to the radius.* **Problem 3**The position of a particle moving in a straight line during a 5-second trip \((0 \leq t \leq 5)\) is given by:\[ s(t) = t^2 - t + 10 \text{ cm} \]Find a time \(t\) at which the instantaneous velocity is equal to the average velocity for the entire trip.---**Problem 4**A particle moving along a line has its position given by:\[ s(t) = t^4 - 18t^2 \text{ m} \]at time \(t\) seconds (for \( t \geq 0 \)). Determine:1. At which time(s) does the particle pass through the origin?2. At which times is the particle instantaneously motionless (has zero velocity)?---In both problems, \(\mathbf{s(t)}\) represents the position function, \(\mathbf{t}\) represents time, and understanding how to find and relate instantaneous velocity and average velocity is crucial for solving these problems.

The initial velocity of an object Height from which it is…

(Free fall) The position function of the object is given - s(t) = s + vt = 1/2gt², where: 0 s is the initial position in meters from the ground leve 0 is the initial velocity, 0 Use g ≈ 9.8 m/s², t is the time measured in seconds after the object is bei Find the velocity of an object that is released with 0 ini

(Free fall) The position function of the object is given - s(t) = s + vt = 1/2gt², where: 0 s is the initial position in meters from the ground leve 0 is the initial velocity, 0 Use g ≈ 9.8 m/s², t is the time measured in seconds after the object is bei Find the velocity of an object that is released with 0 ini

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Question

### Problem 1.
**(Free fall)** The position function of the object is given by:
\[ s(t) = s_0 + v_0 t - \frac{1}{2} gt^2 \]
where:
- \( s_0 \) is the initial position in meters from the ground level,
- \( v_0 \) is the initial velocity,
- Use \( g \approx 9.8 \, \text{m/s}^2 \),
- \( t \) is the time measured in seconds after the object is dropped.

*Find the velocity of an object that is released with 0 initial velocity from a height of 300 m at the moment it hits the ground. Round your answer to the nearest hundredth m/s.*

### Problem 2.
Find the instantaneous rate of change.
1. *Find the rate of change of the area of a square with respect to its side \( s \) when \( s = 5 \).*
2. *Find the rate of change of the diameter of a circle with respect to the radius.*

**Problem 3**

The position of a particle moving in a straight line during a 5-second trip \((0 \leq t \leq 5)\) is given by:

\[ s(t) = t^2 - t + 10 \text{ cm} \]

Find a time \(t\) at which the instantaneous velocity is equal to the average velocity for the entire trip.

---

**Problem 4**

A particle moving along a line has its position given by:

\[ s(t) = t^4 - 18t^2 \text{ m} \]

at time \(t\) seconds (for \( t \geq 0 \)). Determine:

1. At which time(s) does the particle pass through the origin?
2. At which times is the particle instantaneously motionless (has zero velocity)?

---

In both problems, \(\mathbf{s(t)}\) represents the position function, \(\mathbf{t}\) represents time, and understanding how to find and relate instantaneous velocity and average velocity is crucial for solving these problems.

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