The position vector r→ of a particle of mass m is given by the following equation r→(t)=$$α$$t3i^+$$β$$t2j^$$ , where α$$=103ms$$−$$3$$ , β$$=5ms$$−$$2$$ and $$m=0.1$$ kg. At $$t=1$$ s, which of the following statement $$(s) is (are) true about the particle?

Question

The position vector  r→ of a particle of mass m is given by the following equation r→(t)=$$α$$t3i^+$$β$$t2j^$$ , where  α$$=103ms$$−$$3$$  , β$$=5ms$$−$$2$$  and $$m=0.1$$ kg. At $$t=1$$ s, which of the following statement $$(s) is (are) true about the particle?

Infinity Learn · Accepted Answer

r→ $$=$$α$$t3i^+$$β$$t2j^$$→$$1Velocity$$, v→$$=dr$$→$$dt=3$$α$$t2i^+2$$βt $$j^$$→$$2Acceleration$$, a→$$=dv$$→$$dt=6$$α$$ti^+2$$β$$j^$$→$$3$$ At $$t=1sec$$ From (2): v¯$$=3$$α$$i^+2$$β$$j^=10i^+10j^=r$$→×v→mL→$$=$$α$$t3i^+$$β$$t2j^$$×$$3$$α$$t2i^+2$$βt $$j^0.1$$⇒L→$$=2$$αβ$$t4k^$$−$$3$$αβ$$t4k^0.1=0.1$$αβ$$t4$$−$$k^=$$−$$53t4k^$$→$$4$$ At $$t=1=$$−$$53k^The$$ force F→$$=ma$$→From (3), F→$$=0.120i^+10j^$$  $$=2i^+j^=dL$$→$$dt=203t3$$−$$k^=$$−$$203k^$$

The position vector $\vec{r}$ of a particle of mass m is given by the following equation $\vec{r} (t) = α t^{3} \hat{i} + β t^{2} \hat{j}$ , where $α = \frac{10}{3} m s^{- 3}$ , $β = 5 m s^{- 2}$ and m=0.1 kg. At t=1 s, which of the following statement (s) is (are) true about the particle?

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The position vector r→ of a particle of mass m is given by the following equation r→(t)=αt3i^+βt2j^ , where α=103ms−3 , β=5ms−2 and m=0.1 kg. At t=1 s, which of the following statement (s) is (are) true about the particle?

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The position vector $\vec{r}$ of a particle of mass m is given by the following equation $\vec{r} (t) = α t^{3} \hat{i} + β t^{2} \hat{j}$ , where $α = \frac{10}{3} m s^{- 3}$ , $β = 5 m s^{- 2}$ and m=0.1 kg. At t=1 s, which of the following statement (s) is (are) true about the particle?