The position of a point in time `t` is given by `x=a+bt-ct^(2),y=at+bt^(2)`. Its acceleration at time `t` is

Options

A. `b-c`
B. `b+c`
C. `2b-2c`
D. `2sqrt(b^(2)+c^(2))`

Answer

D

Explanation

Given `x=a+bt-ct^(2)` and `y=at+bt^(2)`
Acceleration in X direction`(d^(2)x)/(dt^(2))=-2c`
and acceleration in Y direction `(d^(2)y)/(dt^(2))=2b`
`:.` Resultant acceleration
`=sqrt(((d^(2)x)/(dt^(2)))+((d^(2)y)/(dt^(2))))=sqrt((-2c)^(2)+(2b)^(2))=2sqrt(b^(2)+c^(2))`