1. The position of a particle for t> 0 is given by 7(t) = ((312) + (-6.5 t³)+(-5 t)) m. Assume all quantities are correct to 3 significant figures. (a) What is the velocity as a function of time t? Think: In terms of derivatives, how is velocity related to the postion vector when expressed as a function of time? v(t)=(6t m +-20+10t OV k) S (b) What is the acceleration as a function of time 't'? Think: In terms of derivatives, how is acceleration related to the velocity vector when expressed as a function of time? a(t)=(6 +-40t (c) What is the particle's velocity at t = 2.1 s? Enter to 3 significant figures m +-301-4) (t=2,1 s)=(12.8 +-83.79 (d) What is its speed at t = 0.9 s and t = 2.8 s? +1.0798 k) S Think: Speed at any instant is the magntitude of instantaneous velocity Enter to 3 significant figures (=0.9 s)/= m /v (t =2,8 s)/= m (e) What is the average velocity between t = 0.9 s and t = 2.8 s? Enter to 3 significant figures Think: What is the formula for the average velocity? T= k

1. The position of a particle for t> 0 is given by 7(t) = ((312) + (-6.5 t³)+(-5 t)) m. Assume all quantities are correct to 3 significant figures. (a) What is the velocity as a function of time t? Think: In terms of derivatives, how is velocity related to the postion vector when expressed as a function of time? v(t)=(6t m +-20+10t OV k) S (b) What is the acceleration as a function of time 't'? Think: In terms of derivatives, how is acceleration related to the velocity vector when expressed as a function of time? a(t)=(6 +-40t (c) What is the particle's velocity at t = 2.1 s? Enter to 3 significant figures m +-301-4) (t=2,1 s)=(12.8 +-83.79 (d) What is its speed at t = 0.9 s and t = 2.8 s? +1.0798 k) S Think: Speed at any instant is the magntitude of instantaneous velocity Enter to 3 significant figures (=0.9 s)/= m /v (t =2,8 s)/= m (e) What is the average velocity between t = 0.9 s and t = 2.8 s? Enter to 3 significant figures Think: What is the formula for the average velocity? T= k

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Vectors

Section: Chapter Questions

Problem 3.62AP: After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of...

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After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by v=1.2i9.8tj where v is in meters per second and t is in seconds. The balls displacement away from the edge of the table, during the time interval of 0.380 s for which the ball is in flight, is given by r=00.3803vdt To perform the integral, you can use the calculus theorem [A+Bf(x)]dx=Adx+Bf(x)dx You can think of the units and unit vectors as constants, represented by A and B. Perform the integration to calculate the displacement of the ball from the edge of the table at 0.380 s.
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