A particle starts from rest at the origin and continues to move along positive $$x-axis$$ with acceleration $$2$$ $$m/s2$$. After some time it starts moving with constant retardation $$3$$ $$m/s2$$ and finally stops at a point on $$x-axis$$. If total time of journey of the particle is $$10$$ $$sec$$, find the time during which the particle is accelerated.

Question

A particle starts from rest at the origin and continues to move along positive $$x-axis$$ with acceleration $$2$$ $$m/s2$$. After some time it starts moving with constant retardation $$3$$ $$m/s2$$ and finally stops at a point on $$x-axis$$. If total time of journey of the particle is $$10$$ $$sec$$, find the time during which the particle is accelerated.

Infinity Learn · Accepted Answer

Vmax⁡$$=0+2t1$$; also $$0=Vmax$$⁡−$$3t2$$∴$$2t1=3t2$$......(1) and $$t1+t2=10$$.....(2), solving, $$t1=6$$ $$sec$$

Instantaneous acceleration

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$V_{\max} = 0 + 2 t_{1}; also 0 = V_{\max} - 3 t_{2}$
$∴ 2 t_{1} = 3 t_{2} ...... (1)$ and $t_{1} + t_{2} = 10..... (2),$ solving, $t_{1} = 6 \sec$

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Instantaneous acceleration

Remember concepts with our Masterclasses.

Vmax⁡=0+2t1; also 0=Vmax⁡−3t2∴2t1=3t2......(1) and t1+t2=10.....(2), solving, t1=6 sec

Ready to Test Your Skills?

free study material

$V_{\max} = 0 + 2 t_{1}; also 0 = V_{\max} - 3 t_{2}$
$∴ 2 t_{1} = 3 t_{2} ...... (1)$ and $t_{1} + t_{2} = 10..... (2),$ solving, $t_{1} = 6 \sec$