People become uncomfortable in an elevator if it accelerates from rest at a rate

Question

People become uncomfortable in an elevator if it accelerates from rest at a rate such that it attains a speed of about 6 m/s after descending 30 meters. What would be the magnitude of its acceleration? ANS: 0.6 m/s 2) A car is traveling due east at 25 m/s at some instant. (a) If it undergoes constant acceleration is 0.5 m/s due east, find its velocity after 8.5 seconds have elapsed. (b) If it undergoes constant acceleration is 0.75 m/s2 due west, find its velocity after 8.5 seconds have elapsed. ANS: (a) 31.4 m/s east; (b) 18.6 m/s east A speedboat moving at 30 m/s approaches a no-wake buoy marker that is 100 m ahead. The slows the boat with a constant acceleration of -3.5 m/s by reducing the throttle. (a) What is the velocity of the boat when it reaches the buoy? (b) How long does it take the boat to reach the buoy? ANS: (a) 14.1 m/s; (b) 4.54s 3) a speed of 20 m/s A truck on a straight road starts from rest and accelerates at 2 m/s until it reaches Then the truck travels for 20 seconds at constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5 seconds. (a) How long is the truck in motion? (b) How far did the truck travel? (c) What is the average velocity of the truck during the motion described? ANS: (a) 35 s; (b) 550 m; (c) 15.7 m/s 4) A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of S m/s' as it comes to rest. (a) From the instant the plane touches the runway what is the minimum time needed before it can come to rest? (b) Can this plane land on a small tropical island airport where the runway is 800 5) meters long? Pick a variable and solve for it,; then compare your answer to the one given in the problem. ANS: (a) 20 s; (b) NO -Explain how you determined the answer is no. An indestructible bullet is fired straight through a board that is 10 cm thick. The bullet strikes the board with a speed of 420 m/s and emerges with a speed of 280 m/s. (a) What is the average acceleration of the bullet through the board? (b) What is the total time that the bullet is in contact with the board? (c) How thick (to the nearest 0.1 cm) would the board have to be to stop the bullet assuming the acceleration through the entire board remains constant? ANS: (a) 4.9x10 m/s; (b) 2.86x10*s; (c) 0.18 m 6) An arrow is shot straight up in the air at an initial speed of 15 m/s. After how much time is the arrow heading downward at a speed of 8 m/s? ANS: 0.7s 7) 8) A student drops a ball from the top of a building, and the ball takes 2.8 seconds to reach the ground (a) What was the balls speed just before hitting the ground? (b) How far did it fall? ANS: (a) 27.4 m/s; (b) 38.4 m

Explanation / Answer

1) v = 6 m/s ; d = 30 m

We know from eqn of motion

v^2 = u^2 + 2 a s

a = (v^2 - u^2)/2S

u = 0 ; v = 6 m/s ; S = 30

a = (6^2 - 0^2)/2 x 30 = 0.6 m/s^2

Hence, a = 0.6 m/s^2

2)u = 25 m/s

(a)t = 8.5 s ; a = 0.75 m/s^2

we know from eqn of motion

v = u + at

v = 25 + 0.75 x 8.5 = 31.4 m/s

Hence, v = 31.4 m/s

b)0.75 m/s^2 ; t = 8.5 s ; direction is opposite now

v = 25 - 0.75 x 8.5 = 18.6 m/s

Hence, v = 18.6 m/s

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