# What is Kinamatics: Definition and 16 Discussions

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1. ### Integrating motion equation to derive displacement

##\frac{dx}{dt} = \frac{dx_i}{dt} + \frac{d^2x}{dt^2}t## Multiplying dt on both sides and integrating we have ##\int_{x_f}^{x_i} dx = \int_{0}^{v_i t} dx_i + \int_{0}^{at} dvt## so ##x_f - x_i = v_it + at^2##, which is not right Where did I go wrong? I understand that if we substitute a for...
2. ### Relative Velocity of a Passenger Hitting the Dashboard in a Car Crash

Where exactly have I gone wrong? I think it is the part where I assume that the person gains the deceleration of the car, but I have no other way to proceed in this case. Also please only use the equations that I have posted below, and it would help if you would not use the equation for...
3. ### Kinematics: two runners with different and non-constant accelerations

1. $$x_{A}(t)=\begin{cases}\frac{1}{2}a_A t^2 & 0\leq t\leq 2.8\\ \frac{1}{2}a_A 2.8^2 +v_A t & t>2.8\end{cases}=\begin{cases}\frac{1}{2}a_A t^2 & 0\leq t\leq 2.8\\ \frac{1}{2}a_A 2.8^2 +a_A\cdot 2.8\cdot t & t>2.8\end{cases}$$ so ##x_A(5)=40## implies ##a_A=\frac{40}{17.92}m/s##. Similarly for...
4. ### Pulley system with relative motion

Well, first I tried to understand the relation between the velocities and accelerations of both bodies and I got that the velocity of ##B## is half the velocity of ##A##. This is because a change in length of the cord "that touches ##A##" must be equal to the change in length of the two cords...
5. ### How can rounding errors affect calculations in stopping distance?

I did the first three questions and found that the ignition distance without breaking would be 75 m, it would take 8.3 seconds to stop the car with a maximum acceleration of -3.0 m/s^2 and you would go 103,75 m if so.
6. ### How to get ##\ddot r## when you have ##r##, ##\theta## and right trig

I have a right triangle: one of the angles is ##60°## (that's ##\theta##), one of the sides is ##40 m## long, and the hypotenuse is equal to the radius. Now I can find an expression for ##r## and that expression is ##r=\frac{height}{sin \theta}##. If I differentiate it, I'll get ##\dot r## and...
7. ### I Calculate the exit force of a bullet leaving the barrel

So, Basic premise is I have 1 input and one output, Energy friom the gunpower burning is input, and the output is the force which pushes the bullet after it is reduced by the friction. m = 12.96 g s = 0.6985 m (barrel lenght) E = 6734 J k = 0.5 (friction coeffcient) I am sorry for lack of...
8. ### Radius of curvature of the trajectory of points A and B

Homework Statement A cylinder rolls without slippage on a horizontal plane. The radius of the cylinder is equal to r. Find the radious of curvature of the trajectory of points A and B. Homework Equations Ciruclar motion equations. ##R=\frac{1}{C}## The Attempt at a Solution First I drew the...
9. ### Calculating Separation of Cars in a Convoy Moving at Max Speed

Homework Statement In a convoy on a long straight level road, 50 identical cars are at rest in a queue at equal separation ## 10 m ## from each other. Engine of a car can provide a constant acceleration of ##2 m/s^2##. And brakes can provide a maximum deceleration of ##4m/s^2##. When an order...
10. ### Trajectory of a particle when its position vector changes

Homework Statement The position vector of a particle changes: Only by its module. Only by its direction. What can be said about the trayectory of the movement of the particle? Obtain the answer analitically. Homework Equations None. The Attempt at a Solution I think that the trayectory...
11. ### Calculate the speed of a point based on a graph

Homework Statement A point moves rectilinearly in one direction. The figure shows the distance s traveled by the point as a function of time. Using the graph, find: The average speed of the point during the movement time. Maximum speed The moment t0 in which the instantaneous speed is equal to...
12. ### A Solving Euler's Principal Axis for Rigid Bodies

When we solve Euler's differential equations for rigid bodies we find the angular acceleration ##\dot{\boldsymbol\omega}## and then the angular velocity ##\boldsymbol\omega##. Integrating ##\boldsymbol\omega## is less straightforward, so we start from a representation of the attitude, take its...
13. ### Picture Posting Help - Tips & Tricks

Help with the picture posted!
14. T

### What does time=0 represent in kinematics

So basically i am confused about time 0 in terms of kinamatics graphs Lets say i throw a ball upwards so what does time t=0 represent, the time after which the ball is released or the time at which ball is about to be released? Secondly in projectile motion if i throw a ball horizontally at a...
15. ### Reference Frames? Putting multiple perspectives in kinamatics in 2D problems

Homework Statement I have this assignment on where I have to make up a scenario and solve for the question. The question is that there is a baby that is being thrown out of building into a moving car, (to keep the baby out of harms way). How fast would the car have to traveling to catch...
16. ### Kinamatics problem oh physics elders

Kinamatics problem please help oh physics elders :) 1. A person shoots off a shotgun so that we know the muzzle velocity is 2,200 ft / sec. If that shooter is standing in such a way that the gun is angled at 15*degrees above a horizontal line 5 feet off the ground. It is given that the...