2.53 CALC The acceleration of a motorcycle is given by az(t) = At - Bt?, where A = 1.50 m/s and B = 0.120 m/s4. The motorcycle is at rest at the origin at time t = 0. (a) Find its position and velocity as functions of time (b) Calculate the maxi- mum velocity it attains.
1. Let az, az, az, a4 are vectors in R3. Suppose that az 3a1 – 2a3 + 84. (a) Are aj, aj, az, a4 linearly independent? (b) Suppose that ai, az, a4 are linearly independent. What is the dimension of the span{a1, az, az, a4}? (c) Is the set of vectors aj, az, az, a4 form a basis of R3? Explain your reasoning. (d) Form a basis of R3 using a subset of ai, a2, a3, 24.
z=e37.cos(4), Ir-st, y=215+t az/az= az/ay= M Dz/as= M dy/as = M Oz/dt = M Dy/at = M az/as= az/at= If you don't get this in 3 tries, you can see a similar example (online). However, try to use this as a last resort or after you have already solved the problem. There are no See Similar Examples on the Exams!
healteu, ULL ME Problem 2.53. Expansion of a gas into vacuum (a) Suppose that a gas expands adiabatically into a vacuum. What is the work done by the gas? (b) Suppose that the total energy of the gas is given by (see (2.24)] (2.248) E-NKT – NA where a is a positive constant. Initially the gas occupies a volume Vi at a temperature Ti. The gas then expands adiabatically into a vacuum so that it occupies a total volume V....
ind az- ind az-
Visiuni Useu Find explicit formulas for sequences of the form az, az, az, ... with the initial terms given below.
For the crystal with primitive vectors, Q1,22, and az, defined in the previous problem, the first vector, b1 of the reciprocal lattice is O (27/a)-î + ſ + Ê) O (27/a)(- +) O (21/a) +- A) O (21/a)(- î - ſ + Â)
What is the mass of 2.53 moles of Al?
Define T: R3 → P2(R) by T(aj, az, az) = (a1 + a2 + az) + (a1 + a2 + a3x + 21x2. Determine if T is invertible and compute the inverse of T if it exists.