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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Finding the least acceleration required for particle $A$ to overtake particle $B$

You have two runners modeled as particles $A$ and $B$ respectively. Say that particle $B$ is ahead of particle A by $10$ m, and particle $B$ has a constant velocity of $5$ m/s. When particle $B$ is $50$ m from the finish line particle $A$ starts to…
Benny
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Elementary motion

A lorry is travelling at $60km/h$ when the brakes are applied. Assuming that the deceleration is uniform, how far has the lorry travelled when its speed is $36km/h$ after $6$seconds. What I did: $s =\frac{(v+u)}2t;$ $s = 80$ $m$ But the answer to…
Orestes Dante
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Velocity-time graph

A car travelling at a constant velocity of $20m/s$ passes a stationary sport car. Ten seconds afterwards the sport car accelerates uniformly at $3m/s²$ to reach a speed of $30m/s$ with which it continues. Find when and where the sport car overtakes…
Orestes Dante
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Solving a non-linear system with 3 variables (kinematics)

I'm trying to find the parametric solutions for a 2-dimensional set of kinematics equations. My params are: Δx, Δy - initial and target positions. Vx, Vy - initial velocity. A - the acceleration magnitude. My variables are: t - time to reach x1,…
ShayDavidson
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Two cars traveling, what are the speeds?

Two cars started from the same point and traveled on a straight course in opposite directions for exactly two hours, at which time they were 208 miles apart. If one car traveled, on average, 8 mph faster than the other car, what was the average…
Samantha
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One dimensional inverse square law - motion of charged particles

I'm working on a simple case of two oppositely charged, equal-mass particles in a 1-dimensional system. It might as well be an electron and positron, but without the case of annihilation on contact. The actual system is two magnetic domain walls of…
j carter
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Solving $a = 4v^2$ subject to the constraint that $v = e$ when $x=1$.

A Year 12 exam features the following problem: The acceleration of a body moving in a straight line is given by $a = 4v^2.$ We're given that $v = e$ when $x=1$. The problem is to find the velocity of the body when $x = 2$. I can't solve it. We can…
goblin GONE
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Kinematics Matching Initial Conditions

The acceleration of a body is given in terms of the displacement $s$ meters as $$a = \frac{2s}{s^2+1}$$ Give a formula for the velocity as a function of displacement given that when $s=1,v = 2.$ $$\therefore \frac{1}{2}v^2 = ln(s^2+1)$$ $$v =…
StopReadingThisUsername
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Calculate decel-rate to avoid collision

Imagine the following scenario: We have 2 carts moving alone a track, initially at x velocity. They are spaced apart by y metres and are both z length. When a cart passes a pre-determined point on the track, it starts to decelerate down to another…
M-R
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Kinematics and Integration

A body is moving through a liquid: $$a = -\frac{v^2}{200}-32\ m/s^2$$ $$v_0 = 40\ m/s$$ Find an expression for the time taken, $T$, for the body to slow down to $V\ m/s$ This is from my math class, where no prior physics knowledge is required.…
StopReadingThisUsername
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Particle moving along an $x$ - axis - Ranking its accelerations

The figure below shows that a particle moving along an $x$ - axis undergoes three periods of acceleration. Without written computation, rank the acceleration periods according to the increases they produce in the particle’s velocity, greatest…
Ron
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Magnitude of velocity

A car travels around a circular track with a radius of $r=250m$. When it is at point $A$ then $V_a=5m/s$ which increases at a rate of $\dot{v}=(0.06t)m/s$. Determine the magnitude of its velocity and its acceleration when it is $1/3$ around the…
Derek Kennington
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Straight line motion: Different acceleration and deceleration rates over a known distance

I have an object that can accelerate at a known rate and decelerate at a different known rate that needs to cover a known distance as quickly as possible. It must start and end stationary so it would have to accelerate at its acceleration rate for a…
Omegatron
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Newtonian dynamics

A particle of mass $m$ is projected vertically upwards with speed $v_0$. The resistance force is of magnitude $m$$\lambda$$v^2$. Show that the particle comes to rest after rising through a distance: $h$ = $1/2\lambda$ $(ln(1+\lambda v_0^2/g)$
dahaka5
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Finding The Speed Of A Train Using Basic Trigonometry.

Question: The wheel of a carriage is 3 feet in diameter and makes 3 revolutions per second; how fast is the train going? I'm gonna walk myself through this and hopefully I get it right... Well for starters, the radius of the wheel is 1.5 feet. So…
iLearnSlow
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