Question
An object is moving east with a constant velocity and is at position $x_{0}$ at time $t_{0}=0 .$ (a) With what acceleration must the object have for its total displacement to be zero at a later time $t$ ? (b) What is the physical interpretation of the solution in the case for $t \rightarrow \infty$ ?
Step 1
Step 1: The displacement of an object moving with a constant velocity $v_0$ and acceleration $a$ is given by the equation $x = v_0t + \frac{1}{2}at^2$. Show more…
Show all steps
Your feedback will help us improve your experience
Surjit Tewari and 83 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
Rectilinear Motion The distance $s$, in meters, of an object from the origin at time $t \geq 0$ seconds is given by $s=s(t)=A \cos (\omega t+\phi),$ where $A, \omega,$ and $\phi$ are constant. (a) Find the velocity $v$ of the object at time $t$. (b) When is the velocity of the object $0 ?$ (c) Find the acceleration $a$ of the object at time $t$. (d) When is the acceleration of the object 0 ?
More About Derivatives
The Chain Rule
An object moves along a coordinate line, its position at each time $t \geq 0$ given by $x(t) .$ Find the position, velocity, and acceleration at time $t_{0} .$ What is the spced at time $t_{0} ?$ $$x(t)=\frac{18}{t+2} ; \quad t_{0}=1$$
The Mean-Value Theorem; Applications of the First and Second Derivatives
Velocity and Acceleration; Speed
Rectilinear Motion An object moves in rectilinear motion so that at time $t \geq 0$ seconds, its distance from the origin is $s(t)=\sin e^{t},$ in feet. (a) Find the velocity $v$ and acceleration $a$ of the object at any time $t$ (b) At what time does the object first have zero velocity? (c) What is the acceleration of the object at the time $t$ found in (b)?
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD