The acceleration of a particle is directly proportional to the time t. At t = 0, the velocity of the particle is v = 17 in/s. Knowing that v = 14 in/s and that x = 22 in when t = 1.0 s, determine, a) equations of motion, b) the velocity, the position, and the total distance traveled when t = 7.0 s.
Added by Laura J.
Close
Step 1
Step 1: Given that the acceleration of the particle is directly proportional to time, we can write the equation of motion as: \[ a = kt \] where \( k \) is the constant of proportionality. Show more…
Show all steps
Your feedback will help us improve your experience
Suman K and 64 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A particle travels along a straight line with a velocity v = (12 - 3t^2) m/s, where t is in seconds. When t = 1 s, the particle is located 10 m to the left of the origin. Part A: Determine the acceleration when t = 8 s. Part B: Determine the displacement from t = 0 to t = 7 s. Part C: Determine the distance the particle travels during the time period given in the previous part.
Timothy J.
Particle acceleration If a particle moves along a coordinate line with a constant acceleration $a$ (in $\mathrm{cm} / \mathrm{sec}^{2}$ ), then at time $t$ (in seconds) its distance $s(t)$ (in centimeters) from the origin is $s(t)=\frac{1}{2} a t^{2}+v_{0} t+s_{0}$ for velocity $v_{0}$ and distance $s_{0}$ from the origin at $t=0 .$ If the distances of the particle from the origin at $t=\frac{1}{2}, t=1,$ and $t=\frac{3}{2}$ are $7,11,$ and $17,$ respectively, find $a, v_{0+}$ and $s_{0}$
Systems of Equations and Inequatities
Systems of Linear Equations in More Than Two Variables
The acceleration of a particle is a constant. At $t=$ 0 the velocity of the particle is $(10 \hat{\mathbf{i}}+20 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$. At $t$ $=4 \mathrm{s}$ the velocity is $10 \hat{\mathbf{j}} \mathrm{m} / \mathrm{s} .$ (a) What is the particle's acceleration? (b) How do the position and velocity vary with time? Assume the particle is initially at the origin.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD