Question

Starting from rest , a boat increases its speed to 4 . 12 m / s with constant acceleration , it takes the boat 4 . 77s to reach this speed , how far has it traveled ?

Answer 1

Remember that the average acceleration formula is:

`a = (v_2 -v_1)/(t_2-t_1)`

We have:

`V_2 = 4.12\ m/s\\\\V_1 = 0\ m/s`

`t_2 - t_1 = 4.77\ m/s`

`a = (4.12-0)/(4.77)`

`a = 0.864\ m/s^2`

Now, The equation for the position of a body as a function of time is:

`x(t) = V_0t + 0.5at^2 + x_0`

Where:

`V_0` = initial velocity

`x_0` = Initial position

`x(4.77) = 0+ 0 + (1)/(2)(0.864)(4.77)^2`

`x = 9.83\ m`

The ship has traveled 9.83 m