A particle moves along X- axis as x = 4(t - 2) + a{(t - 2)^2} Which of following is true ?

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2.Motion in Straight Line

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A particle moves along $X-$axis as $x = 4(t - 2) + a{(t - 2)^2}$ Which of the following is true ?

AThe initial velocity of particle is $4$

BThe acceleration of particle is $2a$

CThe particle is at origin at $t = 0$

DNone of these

Solution

(b) $x = 4(t – 2) + a{(t – 2)^2}$
At $t = 0,\,x = – 8 + 4a = 4a – 8$
$v = \frac{{dx}}{{dt}} = 4 + 2a(t – 2)$
At $t = 0,\;\;v = 4 – 4a = 4(1 – a)$
But acceleration,$a = \frac{{{d^2}x}}{{d{t^2}}} = 2a$

Standard 11

Physics

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Match the following columns.

Colum $I$ Colum $II$

$(A)$ $\frac{dv}{dt}$ $(p)$ Acceleration

$(B)$ $\frac{d|v|}{dt}$ $(q)$ Magnitude of acceleration

$(C)$ $\frac{dr}{dt}$ $(r)$ Velocity

$(D)$ $\left|\frac{d r }{d t}\right|$ $(s)$ Magnitude of velocity

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Colum $I$	Colum $II$
$(A)$ $\frac{dv}{dt}$	$(p)$ Acceleration
$(B)$ $\frac{d\|v\|}{dt}$	$(q)$ Magnitude of acceleration
$(C)$ $\frac{dr}{dt}$	$(r)$ Velocity
$(D)$ $\left\|\frac{d r }{d t}\right\|$	$(s)$ Magnitude of velocity

A particle moves along $X-$axis as $x = 4(t - 2) + a{(t - 2)^2}$ Which of the following is true ?

Solution

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Match the following columns.

Colum $I$ Colum $II$

$(A)$ $\frac{dv}{dt}$ $(p)$ Acceleration

$(B)$ $\frac{d|v|}{dt}$ $(q)$ Magnitude of acceleration

$(C)$ $\frac{dr}{dt}$ $(r)$ Velocity

$(D)$ $\left|\frac{d r }{d t}\right|$ $(s)$ Magnitude of velocity