PHYS 1003 Lecture Notes - Lecture 2: Cross Product, Scalar Multiplication, Volt-Ampere

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26 Dec 2017

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Using differentiation, one equation can be converted to another dr/dt -> instantaneous velocity is the velocity at an instant in time (derivative of displacement) Instantaneous acceleration is the acceleration at an instant in time (derivative of velocity) Speed is a scalar quantity = distance travelled/time o o o. Speeding up when acceleration is in the same direction as the velocity. Slowing down is when acceleration is in opposite direction of velocity. Velocity vector and acceleration vector are never in same directions o o o a= dv/dt = d2r/dt2. Unit vector has a magnitude of 1 (no unit): i, j, k. You can add vectors by adding their components. Differentiation of sine is cos and differentiation of cos is -sin. Notations: newtonian (v = and a = = ) lagrange (v= r1 and a = v1 = r11) and leibnitz (slope of function so v= dr/dv and.

Related Questions

A common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time is plotted on the horizontal axis and velocity on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors have only a single nonzero component in the direction of motion. Thus, in this problem, we will call the velocity and the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion, respectively. Here is a plot of velocity versus time for a particle that travels along a straight line with a varying velocity. Refer to this plot to answer the following question.

What is the average acceleration of the particle over the first 20.0 seconds?

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A fish swimming in a horizontal plane has velocity (4.00i + 1.00j) m/s at a point in the ocean where the position relative to a certain rock is r(initial)=(10.0i - 4.00j)m. After the fish swims for 20.0 s, its velocity is v=(20.0i - 5.00j) m/s. a)What are the components of acceleration? b) What is the direction of acceleration with respect to the unit vector i? c) If the fish maintains constant acceleration, where is it at t=25.0 s, and in what direction is it moving?

A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet.

(a) Find the velocity at time t.

(b) What is the velocity after 1 second?

(d) When is the particle moving in a positive direction?

(e) Find the total distance travelled during the first 6 seconds.

(f) Draw a diagram like a Figure 2 to illustrate the motion of the particle.

(g) Find the acceleration at time t and after 1 second.

(h) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 6.

(i) When is the particle speeding up? When is it slowing down?

FIGURE 2

f(t) = t³ – 8t² + 24t

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PHYS 1003 Lecture Notes - Lecture 2: Cross Product, Scalar Multiplication, Volt-Ampere

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