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MTH132 - Examples: Graphs and Position Functions of Particles, Exercises of Physics

University of Advancing Technology Physics

Examples and problems related to the graphs and position functions of particles in physics. Students are asked to determine when each particle is speeding up or slowing down based on the given graphs. Additionally, students are required to find velocities, accelerations, and distances for various position functions. Useful for university students taking a physics course.

What you will learn

When is particle (a) in example 1 speeding up and when is it slowing down?
Find the velocity of the particle in example 3 at time t = 2 seconds.
When is particle (b) in example 1 speeding up and when is it slowing down?

Find the total distance traveled by the particle in example 3 in the first 8 seconds.
When is the particle in example 3 at rest?

Typology: Exercises

2021/2022

Uploaded on 09/27/2022

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MTH132 - Examples

2.7 Problems

Graphs

Example 1. Graphs of the velocity functions of two particles are shown, where tis measured in seconds.

When is each particle speeding up? When is it slowing down? Explain.

(a) v

(b)

Example 2. Graphs of the position functions of two particles are shown, where tis measured in seconds.

When is each particle speeding up? When is it slowing down? Explain.

(a) s

(b)

MSU 1

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MTH132 - 2.7 Problems Graphs Examples

Example 1.When is each particle speeding up? When is it slowing down? Explain. v Graphs of the velocity functions of two particles are shown, where t is measured in seconds. (a) (^0 1) t (b) v 0 1 t

Example 2.When is each particle speeding up? When is it slowing down? Explain. s Graphs of the position functions of two particles are shown, where t is measured in seconds. (a) (^0 1) t (b) s 0 1 t

MTH132 -Standard Problems Example 3. ExamplesA particle moves according to the position function s(t) = (1 +t t 2 ) on the interval t ≥ 0,

where(a) Find the velocity at time t is measured in seconds and t. s in feet.

(b) When is the particle at rest. (c) When is the particle moving in the positive direction? (d) Find the total distance traveled in first 8 seconds

MTH132 - Example 4.Its height after(a) Find the value of ExamplesA ball is thrown vertically upward on planet X with an initial velocity of 10 meters per second. t seconds is given by a if the ball reaches its maximum height after 5 seconds h(t) = −at 2 + 10t + 1

(b) What is the balls maximum height? (c) When will the ball hit the ground? (d) How fast is the ball traveling when it is 2 meters above the ground on the way down?