Question

The functions = 1 - 61? + 121, Osts 3. gives the position of a body moving on a coordinate line with sin meters and in seconds. a. Find the body's displacement and average velocity for the given time interval. b. Find the body's speed and acceleration at the endpoints of the interval c. When, if ever, during the interval does the body change direction? a. What is the body's displacement for the given time interval? m (Simplify your answer.)

Answer 1

- dets3 b) How speed is given by ay Here displacement is given by, s=+3 6+²+12+ Here, displacement over interval is given by, S(3)- scos ( 39-603) +1263)) - (03-600 +1200)) 27-54 +36-0 503) - 500) > 18 m - Displacement over given in tesval is 18 m. How, Average relocity over given interval is given SC3) - SO 3-0 Average velocity over given time interval is omis. Ve Narg 11 3 - varg = dt det - d (+3_64² +124) 3+2 -12 € +12 (dhantom) so, At point re Atle t = 3, speed is, di le-a = 303)? 12033 +12 = 27-36+12 = 3 ... speed of body cat and points is 3 m/ see Also, ese - Acceleration is given by, d's dt d ( 3t2_12t +12)

d²s d42 = 6t -12 (dth -ntr-) 2 so, At endpoint acceleration is given by, d's 1t:3 = 663)-12= 6 m/ see? de 2 ES Now we Know purticle changes direction when velocity is o. Here, ads velocity ds 37² - 12t + 12 20 dt - ) 34²_12++ 12=0 t²_44+4=0 = (+-2) 2 =0 ie t- 20 t=2 .. At t=26 [0,3] The body changes it's direction.