The position of a particle is F(1) = (3.01²î + 5.0ĵ – 6.0rk) m. (a) Determine its velocity and acceleration as functions of time. (b) What are its velocity and acceleration at time t = 0?
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- Alice is riding a bike at 12 mph, but decides to sprint. She takes 0.7 s to accelerate to 19 mph. At constant acceleration, calculate her acceleration, a/(ft/s2). (Here are possibly convenient conversion aids: 60 mph = 1 mi/min = 88 ft/s. This equation is exact. You may wish to verify the equation. One mile = 60*88 ft, and one hour = 60*60 s.)An object undergoes acceleration 2.3i +3.6j m/s² for 5.9 s at which time its velocity is 33i +15j m/s. What was the object's speed at the beginning of the 5.9 s interval?The position of an object moving along an x axis is given by x = 3.18 t-4.04 +1.03 t³, where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object's displacement between t = 0 and t = 4 s? (f) What is its average velocity from t = 2 stot = 4s? (a) Number (b) Number (c) Number (d) Number (e) Number 0.17 i-1.68 0.27 12.70 12.70 (f) Number i 7.19 Units Units Units Units Units Units m m 3 [[|] 3 m/s
- The acceleration of an object (in m/s2) is given by the function a(t)=7sin(t)a(t)=7sin(t). The initial velocity of the object is v(0)=−1v(0)=-1 m/s. Round your answers to four decimal places. v(t) = -7cos(t) + 6 The objects displacement from time 0 to 3 is: 17.01216 meters Find the total distance traveled by the object from time 0 to time 3.An object's position as a function of time in one dimension is given by the expression; 3.89t2 + 2.22t + 7.48 where are constants have proper SI Units. What is the object's average velocity between the times t = 3.16 s and t = 8.38 s?An object's position in the as a function of time obeys the equation; x(t) = 14.2/t2.17 + 5.1t3 where all constants have proper SI Units. What is the speed of the object in the x direction at t = 1.93 seconds?
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- An object's position as a function of time in one dimension is given by the expression; 3.89t2 + 2.22t + 7.48 where are constants have proper SI Units. What is the object's average velocity between the times t = 3.16 s and t = 8.38 s? with everything in 3 sig figsThe acceleration of a particle is a constant. At t=0 the velocity of the particle is (14.91 + 18.4ĵ) m/s. At t = 4.6 s the velocity is 11.4j m/s. (Use the following as necessary: t. Do not include units in your answers.) (a) What is the particle's acceleration (in m/s²)? = î+ 18.4 v(t) = (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin. r(t) = î+ X Î- i) m/s m/sA runner with a good awareness of her pace runs along a path of unknown length at a speed of 0.1250.125 mi/min and then walks back to her starting point at a speed of 0.04500.0450 mi/min. She neglects to note her time for each part of her path but does measure the total round-trip time to be 50.050.0 min. How far did she run? (Do not include walking distance.)