Q1/ The table given below reveals the velocity V of a body during the specified time t. Find the acceleration at t=1.1 t: time V: velocity 43.1 1 1.1 1.2 52.1 1.3 1.4 47.7 56.4 60.8
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- You stand on the seat of a chair and then hop off. (a) Duringthe time interval you are in flight down to the floor, theEarth moves toward you with an acceleration of what orderof magnitude? In your solution, explain your logic. Modelthe Earth as a perfectly solid object. (b) The Earth movestoward you through a distance of what order of magnitude?You're an investigator for the National Transportation Safety Board, examining a subway accident in which a train going at 90 km/hkm/h collided with a slower train traveling in the same direction at 24 km/hkm/h . Your job is to determine the relative speed of the collision, to help establish new crash standards. The faster train's "black box" shows that it began negatively accelerating at 2.1 m/s2m/s2 when it was 52 mm from the slower train, while the slower train continued at constant speed. What do you report ?A 9 kg object starting from rest falls througha viscous medium and experiences a resistiveforce R = −b v, where v is the velocity of theobject.The acceleration of gravity is 9.8 m/s^2.a) If the object’s speed reaches one-half its terminal speed in 5.24s, determine the terminalspeed.Answer in units of m/s. b) At what time is the speed of the object threefourths the terminal speed?Answer in units of s. c) How far has the object traveled in the first 5.24s of motion?Answer in units of m.
- Can you also help w C? C: Determine the direction of the velocity of the sandbag at a time 0.285 ss after its release. TIADr. John Paul Stapp was a U.S. Air Force officer who studied the effects of extreme acceleration on the human body. On December 10, 1954, Stapp rode a rocket sled, accelerating from rest to a top speed of 282 m/s (1015 km/h) in 5.00 s and was brought jarringly back to rest in only 1.40 s. Calculate his (a) acceleration in his direction of motion and (b) acceleration opposite to his direction of motion. Express each in multiples of g (9.80 m/s2) by taking its ratio to the acceleration of gravity.A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = 0.01t4 − 0.03t3 (a) Find the velocity at time t (in ft/s).v(t) = (b) What is the velocity after 1 second(s)?v(1) = ft/s(c) When is the particle at rest? t = s (smaller value) t = s (larger value) (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Find the total distance traveled during the first 11 seconds. (Round your answer to two decimal places.) ft(f) Find the acceleration at time t (in ft/s2). a(t) = Find the acceleration after 1 second(s). a(1) = ft/s2 (g) Graph the position, velocity, and acceleration functions for the first 11 seconds. (h) When, for 0 ≤ t < ∞, is the particle speeding up? (Enter your answer using interval notation.) When, for 0 ≤ t < ∞, is it slowing down? (Enter your answer using interval notation.)
- The automobile is originally at rest, i.e., s (t = 0 s) = 0 m. If it then starts toincrease its speed at a (t) = (0.05t2 ) ft/s 2 , where t is in seconds, then determine the magnitudes ofits velocity and acceleration at s = 550 ft. Note that a (t) becomes a t (t) along the circular path.A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = t3 − 15t2 + 72t (a) Find the velocity at time t. v(t) = (b) What is the velocity after 5 s? v(5) = ft/s (c) When is the particle at rest? t = s (smaller value) t = s (larger value) (d) When is the particle moving in the positive direction? (Enter your answer in interval notation.) t (e) Find the total distance traveled during the first 8 s.ft(f) Find the acceleration at time t. a(t) = Find the acceleration after 5 s. a(5) = ft/s2 (g) Graph the position, velocity, and acceleration functions for the first 8 s. (h) When, for 0 ≤ t < ∞, is the particle speeding up? (Enter your answer in interval notation.) When, for 0 ≤ t < ∞, is it slowing down? (Enter your answer in interval notation.)"In 1865, Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.97 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time.)" Also "Compare your answer with the free-fall acceleration, 9.80 m/s2."
- In a classic clip on Americas Funniest Home Videos, a sleeping cat rolls gently off the top of a warm TV set. Ignoring air resistance, calculate the position and velocity of the cat after (a) 0.100 s, (b) 0.200 s, and (c) 0.300 s.In 1865, Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.97 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time.) Compare your answer with thr free-fall acceleration, 9.80 m/s^2A truck traveling along a straight ,level road at 45 miles per hour when the driver is forced toapply the brakes to avoid an accident. If the brakes supply a constant deceleration of 22 ft/s2,determinea.) the expressions for the truck’s velocity v and position c at anytime tb.) how long will it take to stop?c.) how far does the car travel before coming to a complete stop?ANS.:a.) v(t) = 66 – 22t and s(t) = 66t – 11t2 ; b.) 3 sec. ; c.) 99