Question

A motorboat, initially traveling at 5 m/s, accelerates (speeds up) at 10 m/s^2 over a distance of 500 m. What is the speed of the motorboat at the end of that 500 m?

Answer 1

100.12m/s

Step-by-step explanation:

A body that moves with constant acceleration means that it moves in "a uniformly accelerated motion", which means that if the velocity is plotted with respect to time we will find a line and its slope will be the value of the acceleration, it determines how much it changes the speed with respect to time.

When performing a mathematical demonstration, it is found that the equations that define this movement are as follows.

`\frac {Vf^(2)-Vo^2}{2.a} =X`

where

Vf = final speed

Vo = Initial speed

=5m/s

A = acceleration

=10m/s^2

X = displacement

=500m

solving for vf

`Vf=√(Vo^2+2aX) \\Vf=√(5^2+2(10)(500)) \\\\Vf=100.12m/s`

the speed of the motorboat at the end of that 500 m is 100.12m/s