Simple acceleration question, I think.

[neoncrazy101]

Homework Statement

A person in a kayak starts paddling, and it accelerates from 0 to 0.735 m/s in a distance of 0.400 m. If the combined mass of the person and the kayak is 76.0 kg, what is the magnitude of the net force acting on the kayak?

Homework Equations

F=Ma (?)

The Attempt at a Solution

At first, I tried to figure out the acceleration which for some reason I can't seem to get. I thought I could just do .735/.4 = 1.8375 but its not right. The only equations in my book to get the acceleration requires time which I am not given any in the problem. I even tried doing (.735-0)/(1.8375-0) but it wouldn't give me the correct answer. I know the acceleration should be .68m/s^2 but I can't seem to get to that answer. help?

 

[ldamewood]

It seems like you understand the basic situation of the problem. In order to find the net force, you need the acceleration of the kayak.

I thought I could just do .735/.4 = 1.8375 but its not right.

I hope you realize why you cannot do this. In case you don't, you are trying to divide velocity by distance: this does not give you acceleration (you can check the units).

You are given many equations relating acceleration to time and velocity to time and distance to time: one is the constant acceleration equation for distance;
x_f = x_i + v_i t + 1/2 a t^2.
So, you are given the distance traveled (x_f-x_i) and the initial velocity (v_i=0). Another equation relates the change in velocity to the acceleration:
v_f=v_i + a t
where you know both the initial and final velocity. You now have two equations and two unknowns (a and t are unknown in both equations). You can then use algebra to solve for "a" but it is not straight forward if your algebra is not very strong. I would strongly recommend solving for "a" before plugging in numbers. It is easier to catch algebra mistakes this way. You should also check that your final equation for "a" has units that make sense.

There is also an equation that might be provided for you already (it is the result of doing what I said to do above): it relates "a" to v_f, v_i and x_f-x_i.