If a ship travels along a curved path of radius 350 m with its speed increasing at a rate of 1000 km/h², find the magnitude of acceleration when the speed is
70 km/h.

a. 1.049 m/s²
b. 1.083m/s²
c. 1.079 m/s²
d. 1.069 m/s²

Given data:
v   - velocity of the ship = 70 km/h
a_t - tangential acceleration of the ship = 1000 km/h²
r   - radius of curved path = 350 m = 0.35 km

Let a_n be the normal component of acceleration
The expression for a_n is
a_n = v²/r = 70²/0.35 = 14000 km/h²

The expression for a is given as
a = a_t u_t + a_n u_n
where u_t and u_n are unit vectors in the tangential and normal directions

The magnitude of a is given by


The magnitude of acceleration of the ship when the speed is 70 km/h is 1.083 m / s²