Answered: An acceleration vs. time graph for an…

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter1: Measurement

Section: Chapter Questions

Problem 7FIB

See similar textbooks

Related questions

Concept explainers

Question

100%

An acceleration vs. time graph for an object moving along a line is shown. The value of T = 8.0 s and the value of A = 11.0 m/s².

The object is moving at v = 0.8 m/s at time t=0 s from initial position x = -1.34 m. The graph shown is sinusoidal (meaning it can be written as a sine function or a cosine function) and assumed to continue for all time.

(A) Please determine the acceleration as a function of time for the object.

(B) Please determine the velocity as a function of time for the object

(C) Please determine the position as a function of time for the object

Expert Solution

Part (A)

Given

The amplitude of the graph or maximum acceleration is $A = 11 m / s^{2}$ .
The time period of the graph is $T = 8 s$ .
The initial velocity of an object is $v_{1} = 0.8 m / s$ .
The initial position of an object is $x_{1} = - 1.34 m$ .

The angular frequency is calculated as,

$\begin{array}{rcl} ω & = & \frac{2 π}{T} \\ = & \frac{2 π}{0.8 s} \\ = & 7.85 rad / s \end{array}$

The graph is shown the sine wave. The acceleration of the object is calculated as,

$a = A \sin (ω t + ϕ)$

Substitute t=0 and a=0,

$\begin{array}{rcl} 0 & = & A \sin (ω \times 0 + ϕ) \\ A \sin ϕ & = & 0 \\ \sin ϕ & = & 0 \\ ϕ & = & 0 \end{array}$

Therefore the acceleration is calculated as,

$\begin{array}{rcl} a & = & A \sin (ω t) \\ = & 11 m / s^{2} \times \sin (7.85 t) \end{array}$

Thus, the acceleration as a function of time for the object is $11 \sin (7.85 t)$ .

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Recommended textbooks for you

An Introduction to Physical Science

Physics

ISBN:

9781305079137

Author:

James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:

Cengage Learning