Question

PHYS201 Homework Week 1: motion in one dimension January 24, 2019 To be handed in on Monday Jauuary 28. 1. Graphical description of motion (15 points) (a) For 0 sts 5 s, plot a graph of the position (x) of an object as a function of time (1) for when (i) the object is at rest at r +2, (ii) the object is moving with velocity v 1 m/s (r 0 at 0), (iii) and the object is moving with velocity u-一0.5 m/S (z = +1 m at t = 0). (b) At t = 0 an object is atェ= 0 and it has a velocity of u = 1 m/s. At 1 = 2.5 s, the velocity becomes u 0 and at t = 6 s is becomes u =-2 m/s. At 1 10 s the object comes to rest. Plot the graphs of z and v as a function of t for the time interval 0sts 10 s. What is the total displacement after 10 s? 2. Linear motion at constant (average) speed (25 points) (a) An object is moving at a constant speed of v 4.5 m/s. What is the displacement after t8 s, and how much time does the object need at that speed to travel 1 km? (b) The distance from Lafayette to New Orleans is 220 km. Calculate how long it will take you to drive to New Orleans if you are driving at an average speed of 110 km/h. How much time will you save if you go 120 km/h? (c) A friend of yours starts driving from New Orleans towards Lafayette at the same time when you start your trip to New Orleans. After how much time will you meet if their speed is 90 km/h? 3. Linear motion with constant acceleration (20 points) Consider an object that is accelerating with constant acceleration a. The initial velocity of the object isr(に)-5 m/s. (a) Calculatehow long it takes to bring the object to rest when (i) a0.5 m/s; (ii) a-1 m/s; and (ii) when a 5 m/s. (b) If the object was initially at r12 m when we started observing it (0), where will it be after 10 s if we apply the three previous accelerations (-0.5, -1, and -5 m/s2), and what will its instantaneous velocity be?

Answer 1

a) v = 4.5 m/s, t = 8 sec if d = 1 km = 1000 m of velocity v = dx/dt rightwardsdoublearrow dx = v dt Integrating both side integral_x_1^x_2 dx = integral v dt [v = constant] x_2 - x_1 = v[t_2 - t_1] v = 4.5 m/s given t_1 = 0, t_2 = 8 sec, x_2 - x_1 = Distance/travelled Delta x = 4.5 times 8 Delta x = 32 m. similarly v = x/t rightwardsdoublearrow t = x/v t = 100/4.6 [x = 1 km = 1000 m v = 4.5 m/s t = 222.22 sec time taken to travel 1000 m b) Laf leftarrow 220 km rightarrow New Ore t_Laf to New = 220 km/110 km/r = 32 hrs = 120 sec \r\n if v = 110 km than t_Lafa to New Orlean = 220 km/120 km/r = 1.833 hr = 110 sec Hew saves 10 sec. c) Laf leftarrow 220 km rightarrow New Ore t_A = t_B 220 - x/110 = x/90