Question

For problems #4 and #5, suppose that a particle is moving along the x-axis and that its position at time=1 is given by the function (). Furthermore, suppose that f(2)=-3 and that f(2)=6. No justification required. 4. At time=2, which one of the following statements is true. Write the letter of the correct answer on the answer sheet. No justification required. a) The particle is to the left of x = 0 and the particle is moving to the left. b) The particle is to the right of x = 0 and the particle is moving to the left c) The particle is to the left of x=0 and the particle is moving to the right d) The particle is to the right of x = 0 and the particle is moving to the right e) The particle is to the right of x = 0 and the particle is slowing down. 3. Estimate the value of (2.3). Write the letter of the correct answer on the answer sheet. No justification required. a) 2.3 b) -3.3 C) -2.7 d) 3 C) -1.2 ) -1.8 6. Let /(d) be the noise level (in decibals) of a rock concert at a distance d meters from the concert speakers. What does /(70) mean in practical terms? Write the letter of the correct answer on the answer sheet. No justification required. a) The distance (in meters) from the concert speakers that will result in a noise level of 70 decibels. b) The noise level (in decibels) of a rock concert at a distance 70 meters from the concert speakers. c) The rate of change of noise 70 meters from the concert speakers (in decibels per meter). d) The rate of change of the distance from the concert speakers when the noise is 70 decibels (in meters per decibel) e) none of these 7. Let (1) be the temperature in degrees Celsius at a height of h meters above the surface of the earth. What does T'(400) mean in practical terms? Write the letter of the correct answer on the answer sheet. No justification required. a) The temperature in degrees Celsius at a height of 400 meters above the surface of the earth. b) The height above the surface of the earth at which the temperature is 400 degrees Celsius. c) The rate of change of temperature with respect to height at 400 meters above the surface of the earth (in degrees per meter) d) The rate of change of height with respect to temperature when the temperature is 400 degrees Celsius (in meters per degree) e) none of these

Answer 1

4) f() is the position of the fourtiele, moving along X - anis, at the time t. Given : X 20. f(3) = -3 and f'(2) - 6 So, position of the particle al t = 2 is -3. So, at t=2 the particle will be to the left of f' (2) denotes that the velocity of the particle at t=2². So, f'(2) = 6 gives us that the particle moving along (t)ve x-axis So, option (c) is connect 5 f'(t) e velocity dx dt (Le) da z vdt. So 2.3 77 (du We have to assume the motion of the particle with contant Sa velocity. de z 6 dt 6/dt -3 2 4.] x + 3 z 6 [ 2-3 -2] x z 1.8 - 3 (Option (e) >> x 2 - 1:2

6 at $(d) is the noise level (in decibals) of nock concert a distance & meters from the concent speakers. So, f(70) is the noise level (in decibeb of a rock concent (here we assume there is only one rock concent from the concent speakers. option (6) distance 70 m ent) at 구 T(h) be the temperature in degree Celsius a height of h meters above the sweface of the earth at 2 T'(W) dth) rate of change of T. dh with respect to h. So, T'(400) is the rate of change of temperature with respect to height at 400 m above the sweface of the earth. (in degree Celsium per meten meter). option ©
In (5), as there is no supplied accelaration, we have to assume constant velocity motion of the particle.