At time $$t=0$$, a car moving along a straight line has a velocity of $$16$$ $$ms-1$$. It slows down with an acceleration of $$-0.5t$$ $$ms-2$$, where t is in second. Mark the correct statement (s).

Question

At time $$t=0$$, a car moving along a straight line has a velocity of $$16$$ $$ms-1$$. It slows down with an acceleration of $$-0.5t$$ $$ms-2$$, where t is in second. Mark the correct statement (s).

Infinity Learn · Accepted Answer

$$a=-0.5t=dvdt$$∴ ∫$$16vdv=$$∫$$0t-0.5tdt$$∴ $$v=16-0.25t2s=$$∫$$vdt=16t=0.25t33v=0$$ when $$16-0.25t1=0or$$ $$t=8$$ sSo direction of velocity changes at $$8s$$. Up to $$8s$$ distance $$=$$ displacement∴ At $$4sd=16$$×$$4-0.25$$×(4)33=58.67$$ $$mS8s=16$$×$$8-(0.25)(8)33=85.33$$ $$mS10s=16$$×$$10-(0.25)(10)33$$ $$=76.67$$ cmDistance travelled in $$10$$ s,d $$=(85.33)+(85.33-76.67) $$=94$$ mAt $$10$$ s,  $$v=16-0.25(10)2=-9$$ $$m/s$$∴ Speed $$=9$$ $$m/s$$

At time $t = 0$ , a car moving along a straight line has a velocity of $16 {ms}^{- 1}$ . It slows down with an acceleration of $- 0.5 t {ms}^{- 2}$ , where $t$ is in second. Mark the correct statement (s).

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At time t=0, a car moving along a straight line has a velocity of 16 ms-1. It slows down with an acceleration of -0.5t ms-2, where t is in second. Mark the correct statement (s).

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At time $t = 0$ , a car moving along a straight line has a velocity of $16 {ms}^{- 1}$ . It slows down with an acceleration of $- 0.5 t {ms}^{- 2}$ , where $t$ is in second. Mark the correct statement (s).