Chapter 16, Problem 24P

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A particle travels along a horizontal path where its velocity is defined by v = 2t² – 4t" where t is in seconds. Find the distance it travels in 3 seconds, its displacement from the origin and distance travelled. Find the time it takes for the particle to stop since it makes a turn during the 3 second period. 0 m, 5.3333 m, 2 seconds

The point P moves along a circular path with radius R. Show that the magnitude of its velocity

1. A body moves such that its acceleration is given by a = 2 + 12t where t is in seconds and ‘ a’ is in m/s2. If the body starts from rest and its velocity after 1 sec is 2 m/s, what is the distance traveled after 4 sec? a. 100 m c. 120 m b. 124 m d. 140 m 2. Find the radius of curvature of r = tan θ when θ = 3π/4 .  a. 2.11 c. 2.24b. 3.11 d. 4.11

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Can you solve this in 30 minutes?

An automobile P is traveling along a circular track of radius R=958.4 m. At position "A" on the track, the automobile has a speed of UA = 10.3 m/s. At this position, the driver of the automobile applies the brakes causing the speed of the automobile to change with distance s traveled along the track according to the following equation: U(S) = VA COS(0.001s) m/s (cos is in radians), where s is given in meters. Determine the magnitude of the acceleration for the driver when the automobile reaches position "B" on the track where "B" is a quarter of the distance around the track from position "A". R B O circular track

Q 1. An object rotates with angular acceleration, a defined as a dw where w is the angular velocity dt do Given that when t = 0, w = wo show that w = wo + at Also the angular velocity w is defined as w dt 1 where v is the angular displacement. Given that when t = u, U = U, then show that e = wot + 1 dp -KịpY where k1 + 0 where y dz Y - 1 Q 2. The pressure P of the atmosphere at an altitude z is given by l di Y-1 is the specific heat constant and kį is a constant. Show that z = 1 K

1- A particle moves along the x axis. Its position varies with time according to the expression x=-41+ 2f where x is in meters and t is in seconds. The position-time graph for this motion is shown in Figure. Note that the particle moves in the negative x direction for the first second of motion, is momentarily at rest at the moment 1 = 1 s, and moves in the positive x direction at times /> 1 s. (A) Determine the displacement of the particle in the time intervals t=0 to 1=1 s and t= 1 s to / = 3 s. B) Calculate the average velocity during these two-time intervals C) determine the instantaneous velocity and instantaneous speed at t= 0.5 s. x(m) Slope = 4 m/s 10 00 8 9 10 O Slope =-2 m/s 1 2 015 t(s)