### Understanding Particle Motion through Acceleration-Time Graph#### Initial ConditionsAt time \( t = 0 \), a particle has a velocity of\[ v = 4.00 \, \text{m/s}. \]The following graph shows the particle's acceleration as a function of time.#### Graph DescriptionThe graph displays acceleration (\( a(t) \)) on the vertical axis and time (\( t \)) on the horizontal axis. The key features include:- The acceleration increases linearly from 0 to \(\ 4 \, \text{m/s}^2 \) over the first 2 seconds.- The acceleration then decreases linearly back to \(\ 0 \, \text{m/s}^2 \) over the next 2 seconds.This forms a triangular shape on the graph.#### Problems to Solvea. **What was the particle’s velocity at \( t = 3.00 \, \text{s} \)?**b. **What was the particle’s instantaneous acceleration at \( t = 3.00 \, \text{s} \)?**c. **What was the average acceleration between \( t = 1.00 \, \text{s} \) and \( t = 3.00 \, \text{s} \)?****Note:** The answers to these questions require understanding the relationship between acceleration, velocity, and time, along with interpreting the provided graph's shape and values.

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Description: ### Understanding Particle Motion through Acceleration-Time Graph#### Initial ConditionsAt time \( t = 0 \), a particle has a velocity of\[ v = 4.00 \, \text{m/s}. \]The following graph shows the particle's acceleration as a function of time.#### Gr

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At time t = 0, a particle has a velocity of m a(t) v = 4.00. The following graph shows the particles S acceleration vs. time. What was the particle's velocity at t = 3.00s ? a. t time(s) 4 b. What was the particle's instantaned acceleration at t = 3.00s ? С. What was the average acceleration between t = 1.00s and t = 3.00s ? 2.

At time t = 0, a particle has a velocity of m a(t) v = 4.00. The following graph shows the particles S acceleration vs. time. What was the particle's velocity at t = 3.00s ? a. t time(s) 4 b. What was the particle's instantaned acceleration at t = 3.00s ? С. What was the average acceleration between t = 1.00s and t = 3.00s ? 2.

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Concept explainers

Displacement, Velocity and Acceleration

In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.

Linear Displacement

The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.

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Question

### Understanding Particle Motion through Acceleration-Time Graph

#### Initial Conditions
At time \( t = 0 \), a particle has a velocity of
\[ v = 4.00 \, \text{m/s}. \]
The following graph shows the particle's acceleration as a function of time.

#### Graph Description
The graph displays acceleration (\( a(t) \)) on the vertical axis and time (\( t \)) on the horizontal axis. The key features include:

- The acceleration increases linearly from 0 to \(\ 4 \, \text{m/s}^2 \) over the first 2 seconds.
- The acceleration then decreases linearly back to \(\ 0 \, \text{m/s}^2 \) over the next 2 seconds.

This forms a triangular shape on the graph.

#### Problems to Solve
a. **What was the particle’s velocity at \( t = 3.00 \, \text{s} \)?**

b. **What was the particle’s instantaneous acceleration at \( t = 3.00 \, \text{s} \)?**

c. **What was the average acceleration between \( t = 1.00 \, \text{s} \) and \( t = 3.00 \, \text{s} \)?**

**Note:** The answers to these questions require understanding the relationship between acceleration, velocity, and time, along with interpreting the provided graph's shape and values.

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