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- The position of a particle moving along the x -axis varies with time according to x(t)=5.0t24.0t3 . Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at t=2.0s , (c) the time at which the position is a maximum, (d) the time at which the velocity Is zero, and (e) the maximum position.Find the following for path A in Figure 3.54: (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish.The position of a particular particle as a given by 1)Determine particle's velocity and acceleration as a time.2)Determine function of time is ji=2t i +3t² j–t°k the m. function of the magnitude of velocity and acceleration at time t=2s. dr dv Hint: V dt dt ||
- 2. We are given the velocity funtion of mouing car Along an east-wed4 highung is V(4) = 3€²-24 where t- hours afterho and distance is measured east is the positive direction, in miles, Note that going A If st) is the position in miles from Norton Tewn Mall and at 1 pm the car was at Norton Town Hall, find S(4) B) What was the average velocity of the car from Zpm to 5 pm! Include units of measurementi ) Set up o formula involving either s(E) or the total distance trave lled by the objét from Ipm to tpm? Answer simpligye v(t) that gves must have s" er v's in it. Do not2/6 The acceleration of a particle is given by a = -kt, where a is in meters per second squared and the time t is in seconds. If the initial velocity of the par- ticle at t = 0 is vo = 12 m/s and the particle takes 6 seconds to reverse direction, determine the mag- nitude and units of the constant k. What is the net displacement of the particle over the same 6-second interval of motion?At time t = 0 a particle starts moving along a line with equation of motion s(t) = t^3−4t^2+ 6, whereS is meters and t is in seconds.a) Give the velocity and acceleration functions.b) What is the velocity at time t = 2?c) When is the acceleration 2 m/s^2?
- a stone is dropped from the deck of a bridge. the sound of the splash reached the deck 3 seconds later. the speed of sound is 342 m/s in still air. a) what is the time the stone travels from the deck to the water surface before the splash? b) what is the height of the deck above the water surface? c) determine the time that the sound travels from tge water surface up the deck after the splash?3.) A PARTICLE IS MOVING ALONG A HORIZONTAL LINE ACCORDING TO THE GIVEN EQUATION.The Equation is S = t^3 - 9t^2 + 15t ; t>=0.where (s) meters is the directed distance of the particle from the originat (t) seconds. where (v) meters per second is the instantaneous acceleration of the particle. 1. FIND (v) AND (a) IN TERMS OF (t).2. MAKE A TABLE THAT GIVES A Description of THE POSITION AND MOTION of the particle, include in the table the intervals of time when the PARTICLE IS MOVING TO THE LEFT AND RIGHT include in the table when the VELOCITY IS INCREASING AND DECREASING include in the table when the SPEED IS INCREASING AND DECREASING include in the table the POSITION OF THE PARTICLE with respect to the origin during these intervals of time. and Show the BEHAVIOR OF THE MOTION3. A particle is projected to the right from the position S = 0, when an initial velocity of 8 m/s. If the acceleration of the particle is defined by the relation a = -0.5 v3/2, where a in m/s2 and v in m/s. Determinea) the distance the particle will have traveled when its velocity is 5 m/sb) the time when v = 1m/sc) the time require for the particle to travel 8m
- Y:OY I | %A. N a rE,VK/s a “.lzain IQ docs.google.com/forms مطلوب A 4 نقاط The position of a particle is defined by x=2t3-18t2+48t-16, where x in m and t in s. Determined 1) when the velocity is zero, 2) the velocity, the acceleration and the total * .distance traveled at t=2s 8, 40, 12, 24 others 8, -40, -12, 24 8, -40, -12, -12 O 8, 40, -12, 12 O 4 نقاط A particle A is accelerate from X=0 with zero initial velocity at a=0.8/v2 + 49, where a, v in m/s and m/s respectively. Determine 1) the position of A at any time. 2) the speed of A at any time.5. Derive a formula that relates the displacement, final velocity, time and constant acceleration of an object in UARM (Uniformly Accelerated Rectilinear Motion). Use that formula to find the time it takes for a particle to attain a velocity of 30" given that the constant acceleration is 6 and the particle's displacement is 25m to the left of the origin. Supnoce on olectron hee an ngoolorotion dofinad by a (t) 20to-t where t ieIII. The velocity-time graph of a particle in one dimension is shown in the figure. Assuming that the particle started at x0 = 0 m, what are the instantaneous position x(t) and velocity v(t) equations (in the form compliant with SI units) that correspond to the interval - from A to B? - from B to D? - from D to E? Roughly sketch the corresponding a-t and p-t ploots for the given v-t plot.