A particle moves along a horizontal path, such that its velocity is given by $$v=3t2-6tm/s$$ where t is the time in seconds. If it is initially located at the origin O, determine the distance travelled by the particle in time interval from $$t=0$$ to $$t=3.5$$ s and the particle's average velocity and average speed during the same time interval.

Question

A particle moves along a horizontal path, such that its velocity is given by $$v=3t2-6tm/s$$ where t is the time in seconds. If it is initially located at the origin O, determine the distance travelled by the particle in time interval from $$t=0$$ to $$t=3.5$$ s and the particle's average velocity and average speed during the same time interval.

Infinity Learn · Accepted Answer

⇒  $$v=0$$  at   $$t=2$$ sFor t<$$2$$ s, velocity is negative. At $$t=2$$ s, velocity is zero and for $$t=2$$ s velocity is positive.$$s1=$$∫$$015vdt=$$∫$$01s3t2-6tdt$$ $$=6.125$$ m $$=$$ displacement upto $$3.5$$ s $$s2=$$∫$$02vdt=$$∫$$023t2-6tdt$$ $$=-4$$ m $$=$$ displacement upto $$2$$ s ∴  $$d=$$ distance travelled in $$3.5$$ s $$=4+4+6.125$$ $$=14.125$$ m  Average speed $$=dt=14.1253.5$$ $$=4.03$$ $$m/s$$  Average velocity $$=s1t=6.1253.5$$ $$=1.75$$ $$m/s$$.

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