A boat with initial position (5i -2j+ 4k) metres relative to port, acceleratesuniformly from initial velocity (4i+ j-3k) m s^-1, for 8 seconds until reaching finalvelocity (12i-7j+13k) m s^-1.a)Find the position of the object after 8 seconds. b) Find the acceleration of the object.

Given,

The initial position of the boat, d_i=(5i-2j+4k) m

The initial velocity of the boat, u=(4i+j-3k) m/s

The time period, t=8 s

The final velocity of the boat, v=(12i-7j+13k) m/s

To find:

a) The position of the object after 8 s

b) The acceleration of the object.

Explanation:

a)

From the equation of motion, the total distance traveled by the object is given by,

On substituting the known values,

Thus the final position of the boat is,

b)

The acceleration of an object is given by,

On substituting the known values,

Final

a) Thus the position of the boat after 8 s is

The acceleration of the boat is