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A particle moves along a straight line and its velocity depends on time as `v = 3t - t^2.` Here, v is in `m//s` and t in second. Find (a) average velocity and (b) average speed for first five seconds. |
Answer» Correct Answer - A::B::C (a) Average velocity= Displacement /Time =`(int_0^5 vdt)/5` `=(int_0^5(3t-t^2)dt)/5` `=-0.833 m//s` (b) Velocity of particle=0 at `t=3s` i.e, at 3s, particle changes its direction of motion. Average speed=(Total distance)/(Total time) =((Distance from 0 to 3s)+(Distance from 3s to 5s))/Time `d_(0-3)=int_0^3(3t-t^2)dt=4.5m` `d_(3-5)=int_3^5(t^2-3t)dt=8.67m` `:.` Average speed =`(4.5+8.67)/5` `=2.63 m//s` |
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