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:

$a = \frac{v_2 -v_1}{t_2-t_1}$

We have:

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

$t_2 - t_1 = 4.77\ m/s$

$a = \frac{4.12-0}{4.77}$

$a = 0.864\ m/s^2$

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

$x(4.77) = 0+ 0 + \frac{1}{2}(0.864)(4.77)^2$

$x = 9.83\ m$

The ship has traveled 9.83 m