Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [kinematics]

For questions on the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.

Kinematics is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.

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A particle moving in a straight line has velocity-displacement equation as $v=5\sqrt {1+s}$. Select the correct alternative.

a) Particle is initially at rest. b) Initial velocity of the particle is 5m/s and particle has a constant acceleration of 12.5m/s^2 c) Particle moves with a uniform velocity d) None of these Correct answer is b Since…
Aditya
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An elevator starts from rest. It’s acceleration is plotted against time. When it comes to rest it’s height above the starting point is

Now velocity can be found by calculating the area under the slope. But that turns out to be 0, which is weird. It’s probably because I haven’t understood reading the graphs yet. It’s a simple question, but I still need help solving…
Aditya
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A person moving east finds wind blowing south. If he moves with thrice the velocity, he finds wind blowing southwest. What's wind speed?

A person moving east finds wind blowing south. If he moves with thrice his velocity without changing direction, then he finds the wind blowing in the south-west direction. Find the magnitude of actual speed of the wind if the velocity of the person…
Aditya
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A particle returns to the starting post after 10s. If the rate of change of velocity during the motion is constant in magnitude

Then it’s location after 7 seconds will be the same as that after-? Now my super-efficient and productive brain (#sarcasm) can figure out that it’s 3 seconds, since it has got a constant velocity and 10-7=3. But I doubt future questions like this…
Aditya
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A particle is fired with velocity u making an angle $\theta$ with the horizontal.

What is the change in speed at the highest point? What is important to notice here, is that the change in speed is asked, not velocity. If it was velocity, the answer is $usin\theta$ (which is way too easy) For speed, directions aren’t important, so…
Aditya
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One second after projection, a stone moves at an angle 45 with the horizontal. Two seconds after projection

It moves horizontally. It’s angle of projection is MY SOLUTION Time of flight is 4sec Therefore $usin\theta=20$ Also after 2 sec, the vertical velocity is zero At one second, the vertical velocity is $\frac{u_0}{\sqrt 2}$ $$0=\frac{u_0}{\sqrt 2} -…
Aditya
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A particle is projected with velocity $v_0$ along $x$-axis. The deceleration on the particle is $a=\alpha x^2$

The distance at the which the particle stops is MY SOLUTION $$a=v\frac{dv}{dx}$$ $$vdv=\alpha x^2 dx$$ Integrating $$\int_{v_0}^0 v\,dv=\int_0^x \alpha x^2\,dx$$ $$-\frac{(v_0)^2}{2}=\alpha…
Aditya
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Solving simultaneous equations for motion

Textbook asked student to solve the following simultaneous equations where x is distance in cm and t is time in minutes: x = 2t x = -4t -20 I multiplied equation 1 by the 't' coefficient of equation 2, -4, and vice-versa multiplied equation 2 by…
H Lachlan
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kinematics .. how to solve this question. shouldn't acceleration be 0 when velocity is 0?

a particle moves in a straight line so that , $t$ s after passing through a fixed point $O$ , its velocity $v$ in $\frac{m}{s}$, is given by $$v = 2t -11-\left(\frac{6}{(t+1)}\right)$$ Find the acceleration of the particle when it is at…
Dexter Khoo Jun Ming
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What is the initial acceleration of three particle at the vertex of an equilateral triangle moving towards its neighbor?

I came across this question which, asks, 3 particles, at the corner of an equilateral triangle of side s, start moving with constant speed v, such that each always heads directly towards its clockwise neighbor. What is the magnitude of the initial…
Nothingham
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Calculate distance travelled with non-constant speed after time t

Let's Imagine such a situation. A man is walking for the first hour with a speed of $4km/h$. The next hour he is jogging, with the speed of $9km/h$ Finally, after two hours, he starts to run, with the speed of $12km/h$ As one might expect, I want to…
Karol Szustakowski
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Finding the time elapsed between the instant when two particles are projected and the instant they collide

So say you have a vertical mast of height $32$m, and then say a particle P is projected horizontally from the top of the mast at $18$ m/s. Then say that a particle Q is projected at $30$ m/s from the bottom of the mast at an angle x above the…
Benny
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Using a vt graph to find the value of a velocity V after a time T with an acceleration of a, and starting velocity at 10 m/s

I am trying to model a situation in which a car passes the point A on a straight road with a speed of 10 m/s, and moves with a constant acceleration of a m/s^2 along the road for T seconds until it reaches the point B where its speed is V m/s. The…
Benny
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How can there be two answers for this problem?

This is a problem involving an equation relating the time it takes for an object to be dropped and the height from which it is dropped (kinematic). I have the following from MyMathLab on Inverse Functions: Notice that plugging in the exact value…
Sphygmomanometer
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Application of calculus in kinematics- calculating net distance vs. total distance ??

There is a set of questions where it says to find the net distance and the total distance from $t_1$ to $t_2$ when the function v(t) is given. I get that you obtain the displacement function s(t) by integrating v(t), but what exactly is the…
minnn
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