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 is projected from the ground at an angle theta with horizontal and some velocity

For any position A, show that $\tan\alpha + \tan\beta =\tan\theta$ MY SOLUTION: We know that $\tan\theta=\frac{4h}{R}$ $$\tan\alpha=\frac{h}{x}$$ And $$\tan\beta = \frac{h}{R-x}$$ So $$\tan\alpha + \tan\beta = \frac{hR}{xR-x^2}$$ That’s as far as I…
Aditya
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The vertical velocity of a ball hit by a bat is given in the following options. Which of them is right?

Which of the above graphs describe the variation of the ball’s velocity v with time between the time t1 as it hits the bat and t2 as it touches the ground? I solved it, and my imperfect visualisation gave me c as the right option. Obviously, and…
Aditya
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How to go about solving a basic mechanics problem?

The bus leaves the bus stop with an acceleration of 1.5 m.s^-2 which is mantained until it reaches the speed of 12 m.s^-1. At the same instant a girl who is 5 m away from the bus stop starts to run after the bus at a constant speed of 7 m.s^-1. Will…
Zayed
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Relationship between angle of banked road and normal force and its component

Why are these two angles in the diagram below equal? I can't quite see their relationship or proof of why they are the same.
Max604
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Find acceleration of a particle when given a velocity function in terms of displacement.

Particle B moves such that its velocity $v\>ms^{-1}$ is related to its displacement $s\>$m, by the equation $v(s)=arcsin(\sqrt{s})$. Find the acceleration of particle B when $s=0.1 $m. My…
Jane T
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A car can accelerate to a Maximum speed $M$ at $1.5 m/s^2$ and brake at $2.0 m/s^2$....

So, the problem goes thusly: a car can accelerate to a maximum speed of $M$, at $1.5 \space \mathrm{m/s}^2$ and brake at $2 \space \mathrm{m/s}^2$. How long does it take to go a thousand kilometers? Also, for my own personal edification, I asked:…
user1833028
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Solving Taking time with acceleration, deceleration and speed.

i currently calculating the total time travel of a servo motor moving from point A to point B. I having a distance with 1000m with speed 10m/s , acc = 2m/s^2 and dcc=2m/s^2, what is the equation for this type of question ? I have use the trapezoid…
user1804079
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Determine the magnitude and the direction of the velocity of the aircraft.

An aircraft A is flying in a vertical plane containing two tracking stations P and Q which are 15km apart. At a cetain instant θ (measured anticlockqise from horizontal line PQ to the line PA) is 60° and the $ \dot \theta $ (angular velocity) is…
S.Dan
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Kinematics Question?

approach: a) $d_{y} = v_{1y}t + 0.5at^{2}$ $680 = v_{1}\sin{57(6.20s)} - 188.55$ $v_{1} = 585 m/s$ im not sure if this is right.. any help is really appreciated! B) not sure how exactly to apprach this :/
Jessica
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Ball being shot backwards off a moving vehicle? Relative motion?

A truck travelling at 80 km/h has a pitching machine firing baseballs backwards off the back. The pitching machine is set to fire at 80 km/h. a) how does a passenger in the truck see the ball move? b) how does a person at the side of the road see…
Jessica
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Any one their to help me to solve this relative velocity question?

Two rail tracks ,which make an angle $X$ with each other ,intersect at $O$. Two trains $P$ and $Q$ are travelling on these tracks with speeds $u$ and $v$ towards $O$. Initially $P$ & $Q$ are at distance $a$ & $b$ from $O$ respectively. Show that…
On the way to success
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finding the greatest distance reached above the ground

question mark scheme answer I don't understand why there is an additional $0.441$ added to the final distance... I do understand that the distance travelled by $A$ downwards is equal to the distance moved by $B$ upwards but why the $0.441$? I solved…
wjkrkdfjkn
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What is the underlying mathematical idea behind Galileo thinking that motion can be studied in terms of projections?

Galileo’s discovery is that from these two simpler motions, in the plane and on the line, he could completely recapture the complicated motion in space. In fact, if the motions of the shadow and the level are ‘continuous’, so that the shadow does…
tryst with freedom
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Is this differential equation solvable$?$

If $$v=\frac{dx}{dt},a=\frac{dv}{dt}=\frac{d^2 x}{d t^2}$$ Then :$$x^2+v^2=a^2$$ Is solvable or not ?
Sushil
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Eastward horizontal acceleration

Exercise 2/99 from 6th Ed of Meriam, Kraige - Engineering reads: An object which is released from rest from the top $A$ of a tower of height $h$ will appear not to fall straight down due to the effect of the earth's rotation. It may be shown that…
Thales
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