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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The speed of a boat is 5Km/h in still water. It crosses a river of width 1km along the shortest path in 15 minutes.

Velocity of the river is? Since it covers 1km in 15 mins, the relative velocity of the boat with respect to the river will be $$\frac 14 V_{br}=1$$ $$V_{br}=4km/h$$ So $$V_b=V_{br} + V_r$$ $$V_r=1km/h$$ The right answer is 3km/h, so what am I…
Aditya
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How long will it take a stone to fall from the top of a tower?

A stone dropped from the top of a tower is found to travel $5/9$ of the height of the tower during the last second of the fall. The time of fall is? Let $T$ be the time it takes for the stone to reach the ground and $h$ be the height of the…
Aditya
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A man of height h walks in a straight path towards a lamp post of heiight H with uniform velocity u.

The velocity of the edge of shadow on ground will be. The answer is $$\frac{hu}{H-h}$$ All I was able to do was draw this measly diagram. It’s an understandably difficult to infer question, if not tough as a whole. Help would be appreciated
Aditya
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A ball is dropped on the ground and bounces back to a height somewhat less than the original height. Which of the curves depicts its motion correctly

The options are given below To me, both options b and c look the same. I know there is bound to be some difference, but I just can’t figure it out. C is the wrong answer while b is right. Both their slopes have the same signs and differ only in…
Aditya
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Physics like question

Question: A train is travelling at $18\ m/s$. However the conductor notices something on the tracks $126\ m$ ahead of the current position. How long can the conductor wait before beginning to brake if the max safe braking rate is $1.8\ m/s^2$? I…
dreamin
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A particle starts its motion from rest and moves with constant acceleration for time $t_1$ and then it retards with constant rate for $t_2$.

And comes to rest. Then the ratio of maximum speed and average speed during the complete motion will be MY SOLUTION Let acceleration be a. Max speed $$v=at_1$$ Also distance covered will be $$s=\frac{(2)(at_1^2)}{2}$$ $$=at_1^2$$ So average speed…
Aditya
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A river flows south with a velocity of 2m/s. A man steers his boat across the river with a velocity of 4m/s to east relative to the river.

Find the orignal velocity of the boat MY SOLUTION: Let’s assume coordinate axes along the conventional directions, where +x is in east and +y is north (although it’s relatively unimportant) Since the relative velocity of boat wrt to river is 4j and…
Aditya
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Equation of motion of a body is $\frac{dv}{dt}=-4v+8$ where is velocity in $m/s$ and $t$ is time.

Initial velocity of the particle was zero. Choose the correct options. OPTIONS A) Initial rate of change of acceleration is 8 B) The terminal speed is $2\text{m/s}$ C) both A and B D) Neither A and B I could find initial acceleration by…
Aditya
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Mechanics-Maths

Particles $A$ and $B$ are moving along horizontal straight lines which lie in the west east direction. At a certain time, $A$ passes a point $P$ moving to the east with speed $5$ ms$^{-1}$ and constant acceleration $1$ ms$^{-2}$. Simultaneously, $B$…
Abdel Moniem
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What are the forward kinematics of moving point on a line between two moving points?

Suppose we have two points $A, B \in \mathbb{R}^2$ where $A = (0 | y)$ and $B = (0|-y)$. Also we have a point $P$ which lies on the line between $A$ and $B$. If we can move the two points on the x-axis at velocity $v_x$ and the point $P$ on the line…
Erdogan Seref
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$n$ particles hunting each other

If $n$ particles $A_1,A_2,...,A_n$ are situated at the vertices (at time $t=0$ $s$ of an $n$ sided regular polygon $\overline{A_1A_2...A_n}$ such that the velocity of the $n^{th}$ particle is always along the side $\overline{A_{n-1}A_n}$ of the…
sato
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Additional IGCSE Kinematics problem, Cambridge Oct/Nov 2011 0606/13

Hi I am having problems with this question below, still have no teacher to help due to corona: A particle moves in a straight line so that, t s after leaving a fixed point O, its velocity vms-1 is given by v = 3e2t + 4t Find the distance travelled…
Hancho
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Acceleration and speed from timed events

Basically I have data from a list which shows how an automated scenery truck should move. The guys in the who have given it have basically given me an acceleration time and deceleration (or negative acceleration) time and a time at full speed they…
SimonW
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Nonholonomic conditions - Rolling disk

Suppose there is a rolling disk subject to non-slipping condition. The kinematic model follow below. \begin{equation} \begin{cases} \dot x = v \, cos(\theta) \\ \dot y = v \, sin(\theta) \\ \dot \theta = \omega \end{cases} \end{equation} If I know…
Bruno Lobo
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A particle moves in such a way that its position varies with time t as $r=ti+\frac{t^2}{2}j+tk$

Find as a function of time the speed of the particle. Since it’s speed, I calculated the magnitude $$D=\sqrt{t^2+\frac{t^4}{4}+t^2}$$ $$D=\frac{t\sqrt{8+t^2}}{2}$$ Differentiating wrt t, I get $$\frac{t^2+4}{\sqrt{8+t^2}}$$ The answer is given…
Aditya
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