y100.103/360050 50/9 The ratio is =057 2. The x-component of the position vector of a particle is shown in the graph in Figure 1 as a function of time (a) The velocity component v at the instant 3.0 s -4m/s b)Is the velocity component zero at any time? yes If so, 4 the time is-15s_. If not, explain why not 2 (c) Is the particle always moving in the same direction along the x-axis? No If so, explain what leads you to this conclusion If not, the positions at which the Fig 1 particle changes direction is x=5m, fl5s Solution:(a) According to the definition of the instantaneous velocity v,= tangent to graph at f3s, So v 6=-4m/s 1.5 (b)Because the tangent at Fl 5s is zero (c) According to the tangent of the graph, the velocity is positive during t<1.5s and negative during 3. When a radio wave impinges on the antenna of your car electrons in the antenna move back and forth along the vx aponent schematically in Figure 2. Roughly sketch the same graph and indicate the time instants when (a)The velocity component is zero,aceg (b) The acceleration component is a, zero; b,d,fh (c) The acceleration has its maximum magnitude Fig2 .C,e, Solution (a)See the graph. (b)c) According to the definition of the acceleration a dv2() tangent to graph, we d drawing the conclusion 4. The graphs in Figure 3 depict the velocity component v of a rat in a one-dimensional maze as a function of time. Your task is to make graphs of the corresponding5.56(m/s ) 9 50 5 100 10 / 3600 2 3 = = ⋅ = ∆ ∆ = t v a The ratio is 0.57 9.81 50 / 9 = 2. The x-component of the position vector of a particle is shown in the graph in Figure 1 as a function of time. (a) The velocity component x v at the instant 3.0 s is -4m/s . (b) Is the velocity component zero at any time? yes If so, the time is 1.5s . If not, explain why not, . (c) Is the particle always moving in the same direction along the x-axis? No If so, explain what leads you to this conclusion. If not, the positions at which the particle changes direction is x=5m, t=1.5s . Solution: (a) According to the definition of the instantaneous velocity t x t vx d d ( ) = , tangent to graph at t=3s, so 4m/s 1.5 6 vx = − = − . (b) Because the tangent at t=1.5s is zero. (c) According to the tangent of the graph, the velocity is positive during t<1.5s and negative during t>1.5s 3. When a radio wave impinges on the antenna of your car, electrons in the antenna move back and forth along the antenna with a velocity component x v as shown schematically in Figure 2. Roughly sketch the same graph and indicate the time instants when (a) The velocity component is zero; a, c, e, g (b) The acceleration component is ax zero; b, d, f, h (c) The acceleration has its maximum magnitude. a, c, e, g Solution: (a) See the graph. (b)(c) According to the definition of the acceleration t v t a x x d d ( ) = , tangent to graph, we can drawing the conclusion. 4. The graphs in Figure 3 depict the velocity component x v of a rat in a one-dimensional maze as a function of time. Your task is to make graphs of the corresponding 0 1 3 2 2 4 t(s) x(m) Fig.1 vx t Fig.2 a b c d e f g h