A particle is traveling along the curve y = e ^{- x}  with a constant velocity of 25 m / s. Determine the particle's acceleration at x = 1.

a ) 198.97 m / s²
b ) 160.50 m / s²
c ) 192.23 m / s²
d ) 189.97 m / s²

For the curve e ^{- x}  the instantaneous radius of
curvature at x = 1 is given by,

Since the particle is traveling with a constant
tangential velocity it has no tangential acceleretion.
Hence the acceleration of the particle is due to the
normal acceleration a _n only.

The particles acceleration at x = 1 is 189.97 m / s²