A particle starts from the origin at t=0 and moves along the...

A particle starts from the origin at $t=0$ and moves along the positive $x$ axis. A graph of the velocity of the particle as a function of the time is shown in Fig. $2-46 ;$ the $v$ -axis scale is set by $v_{s}=4.0 \mathrm{~m} / \mathrm{s}$. (a) What is the coordinate of the particle at $t=5.0 \mathrm{~s} ?(\mathrm{~b})$ What is the velocity of the particle at $t=5.0 \mathrm{~s} ?(\mathrm{c})$ What is the acceleration of the particle at $t=5.0 \mathrm{~s} ?(\mathrm{~d})$ What is the average velocity of the particle between $t=1.0 \mathrm{~s}$ and $t=5.0 \mathrm{~s} ?(\mathrm{e})$ What is the average acceleration of the particle between $t=1.0 \mathrm{~s}$ and $t=5.0 \mathrm{~s}$ ?

Key Concepts

Average Acceleration

Average acceleration is defined as the change in velocity divided by the corresponding change in time over a given interval. It gives a measure of how the velocity is changing on average between two points in time.

Average Velocity

Average velocity is calculated as the total displacement divided by the total time elapsed. It represents the overall rate of position change over a specified time interval and can differ from instantaneous velocity at any specific moment.

Instantaneous Acceleration

Instantaneous acceleration is the rate at which the object's velocity is changing at a particular instant. It is found by calculating the derivative of the velocity function with respect to time, or by determining the slope of the tangent line on the velocity-time graph at a given point.

Instantaneous Velocity

Instantaneous velocity is the speed of the object at a specific point in time. It can be directly read off a velocity-time graph at any given time, providing a snapshot of the object's motion at that moment.

Displacement

Displacement refers to the change in the object's position and is calculated by taking the integral of the velocity with respect to time. On a velocity-time graph, it is determined by the area under the curve between two time intervals.

Velocity-Time Graph

A velocity-time graph is a visual representation that shows how the velocity of an object changes over time. It is used to determine displacement by calculating the area under the curve, as well as to identify instantaneous values of the velocity at any particular moment in time.