A particle moves in an XY-plane in such a way that its x and y-coordinates vary with time according to
`x(t)=t^(3)-32t, y(t)=5t^(2)+12`
Find the acceleration of the particle, if t = 3 s.

Options

A. `9 hat(i)+5 hat(j)`
B. `18hat(i)+10hat(j)`
C. `18hat(i)-5hat(j)`
D. `-18hat(i)+10hat(j)`

Answer

B

Explanation

The coordinates of the particle is given as
`x(t)=t^(3)-32` and `y(t)=5t^(2)+12`
where, t = time
The velocityat time t,
`upsilon_(x)(t)=(dx(t))/(dt)=3t^(2)-32`
`rArr a_(x)(t)=(d upsilon_(x)(t))/(dt)=6t-0=6t`
At `t=3, a_(x)=6xx3=18`
and `upsilon_(y)(t)=(dy(t))/(dt)=10t+0=10t`
At `t=3, a_(y)=10`
Thus, `a=a_(x)hat(i)+a_(y)hat(j)=18hat(i)+10hat(j)`