The motion of a particle along a straight line is described by equation : x $$=$$ $$8$$ $$+12t$$ $$-t3$$ where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

Question

The motion of a particle along a straight line is described by equation : x $$=$$ $$8$$ $$+12t$$ $$-t3$$ where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

Infinity Learn · Accepted Answer

v $$=$$ dxdt $$=$$ $$12-3t2$$     $$---(i)If$$ velocity is zero, $$12-3t2$$ $$=$$ $$0$$ which gives t $$=$$ $$2$$ secFor acceleration again differential equation $$(i)a$$ $$=$$ $$d2xdt2$$  $$=$$ $$-6t----(ii)At$$ time t $$=$$ $$2$$ $$sec$$, a $$=$$ $$-6$$×$$2$$ $$=$$ $$-12$$ $$m/s2Hence$$ retardation $$=$$ $$12$$ $$m/s2$$

The motion of a particle along a straight line is described by equation : $x = 8 + 12 t - t^{3}$ where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

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The motion of a particle along a straight line is described by equation : x = 8 +12t -t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

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The motion of a particle along a straight line is described by equation : $x = 8 + 12 t - t^{3}$ where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is