EXAMPLE 6 A particle moves along a line so that its velocity at time t is v(t) = - + - 12 (measured in meters per second

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Example 6 A Particle Moves Along A Line So That Its Velocity At Time T Is V T 12 Measured In Meters Per Second 1 (42.62 KiB) Viewed 24 times

EXAMPLE 6 A particle moves along a line so that its velocity at time t is v(t) = - + - 12 (measured in meters per second) (a) Find the displacement of the particle during 2 sts 10. (b) Find the distance traveled during this time period. SOLUTION (a) By this equation, the displacement is s(10) - $(2) = v(t) dt 10 10 - [") (t2-1-12) dt 710 13 3 - - 12] එය 186.66 X This means that the particle moved approximately 186.67 meters to the right. (b) Note that v(t) = 2 - - 12 = (t - 4)( + 3) and so v(t) SV O on the interval [2, 4] and v(t) 2V Oon [4, 10). Thus, from this equation, the distance traveled is -10 IV() [-vt] dt + . 10 () dt 10 I live "ivel dt = f*i-vey) at * ["vce - + - - +1+ 12) at ["d - - 12 [ + - ) - [ -$++126 1+1 % - -12 - t dt + -- ) đt 110 } 2 2 + 2 2 - 3 3 210.67