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Second Law of Motion

The motion of...

Question

The motion of a particle is given by
$X = 5 + 10 t + 17 t^{2} + 4 t^{3}$
$Y = 8 + 9 t + 20 t^{2} - 6 t^{3}$
The force on the particle is :

zero

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parallel to x-axis

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parallel to y-axis

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varies with time

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Solution

The correct option is C varies with time
Force on particle = ma , where a is acceleration of particle.
acceleration in direction $X$ ,
$a_{X}$ = $\frac{d^{2} X}{d t^{2}}$ = 34+ 24 $t$

acceleration in direction $Y$ ,
$a_{Y}$ = $\frac{d^{2} Y}{d t^{2}}$ = 40-36 $t$
Acceleration is varying with time $t$ . So the force on the particle is varies with time.

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