Essential Mathematics: Dynamics

15 flashcards · Mathematics · by lakesare

  1. What's a vector function?

    A function that returns vectors. A vector function is a function whose output values are vectors.Its input values can be scalars, like times, or vectors.

  2. When does velocity increase and decrease, VS speed increase and decrease? When you are working with graphs of position, velocity and acceleration, it is important to remember that velocity is not the same as speed.

    velocity - decreasing throughout the whole 2 seconds, speed - decreasing t∈[0, 1], and increasing t∈[1, 2]. Although the velocity of the particle is decreasing throughout the whole two second time interval, the speed of the particle is decreasing between t = 0 and t = 1, and increasing between t = 1 and t = 2.

  3. [Interpreting a velocity–time graph] If the particle starts (at time t = 0) at the origin, is its position positive or negative at time t = 4? The graph shows the velocity (in m/s) of a particle against time (in seconds).

    Position at t = 4 is negative, since the area below the x-axis is larger than the area above the x-axis. The change in the position of the particle from time t = 0 to time t = 4 is the signed area between the velocity–time graph and the t-axis from time t = 0 to time t = 4. Since the area below the x-axis is larger than the area above the x-axis, the change in the position is negative. So, since the particle starts at the origin, it finishes at time t = 4 with a negative position.

  4. [Equations of motion] What are the assumptions behind the equations below?

    These are equations of motion for constant acceleration! People often forget that the kinematic formulas are only true assuming the acceleration is constant during the time interval considered.

  5. [Interpreting a position–time graph] At approximately what time is the speed of the particle greatest?

    At 2.75 seconds. The speed is greatest at the time when the magnitude of the gradient of the position–time graph is the greatest. This is at time approximately 2.75 seconds.

  6. [Interpreting a position–time graph] At approximately what time does the direction of motion of the particle reverse?

    At 2 seconds. The position x of the particle increases until approximately time t = 2, after which it decreases. So the direction of motion of the particle reverses at time approximately 2 seconds.

  7. [Using Newton's second law to predict motion] How would you go about finding how far the toy moves in the first 3 seconds?

    Start by finding the acceleration, then the velocity, then the position, in terms of time.

  8. What friction is typically higher - static or dynamic? Sliding friction is also known as dynamic friction or kinetic friction.

    Static friction is usually higher! It's harder to start objects moving than it is to keep them moving. The coefficient of sliding friction between two materials is always less than the coefficient of static friction between the same two materials. This accords with our everyday experience that it is harder to start objects moving than it is to keep them moving.

  9. What's the formula for static friction VS dynamic friction? Sliding friction is also known as dynamic friction or kinetic friction.

    Static friction: Fmax = μ * N μ - coefficient of static friction.Dynamic friction: F = μ * N μ - coefficient of dynamic friction. Like a static friction force, a sliding friction force acts to oppose motion, though unlike a static friction force its magnitude does not adjust to balance other forces in any way.

  10. [Working with sliding friction] Why does mass not affect acceleration? A skier slides under gravity down a straight ski slope covered in wet snow, which is inclined at an angle of 30◦ to the horizontal. The coefficient of sliding friction between the skis and the snow is µ = 0.04. Find the magnitude of the skier's acceleration (to 2 s.f.).

    Because Fres = m * smth + m * smth ares = Fres/m

  11. [Determining velocity from position]

  12. [Determining position from velocity] Write down how to solve this with the right syntax.

  13. How is it possible that the speed is constant, but object is accelerating?

    Acceleration is a rate of change of its velocity - meaning objects that changes its direction is accelerating. Because the acceleration of an object is the rate of change of its velocity, an object is accelerating if either its speed is changing or if the direction of its velocity is changing, or both. In particular, an object that is moving with a constant speed but with a changing direction is accelerating. For example, an object that is moving with a constant speed along a circular path is a…

  14. [The third derivative of position with respect to time] r' = speed r'' = acceleration What's r'''?

    A jerk. Change of acceleration with respect to time is called a jerk. Passengers travelling in a vehicle experience non-zero jerk – that is, changing acceleration – as discomfort. For example, you experience non-zero jerk for a short time when a vehicle that you are travelling in stops suddenly. If a train travels at a constant speed along a straight track, then its acceleration is zero, so its jerk is also zero. If it travels at a constant speed along a track that is an arc of a circle, then i…

  15. What's a range of the projectile?

    Distance travelled along the ground.