Jennifer jogs at constant speed of of 3.2 meters per second to her neighbor's house down the block, which is 530 meters away. How long did it take her to get there?
The secret to solving word problems is to G.U.E.S.S.!
Before we continue, take a look and notice that you have translated to word problem to a regular problem. Yay!
Once you are done GUESSing, you will have the answer to your word problem. Now let's see how it works!
Reading the probelem gives us this information:
The only quantity that isn't explicitly stated, and has to be inferred, is the acceleration. We look for the context clue of "constant speed", which we should interpret as "zero acceleration".
To see why this is, we can look at the definition for acceleration: $a \equiv \frac{v_f - v_i}{t_f - t_i}$. Since velocity (or speed in this case) is constant, then $v_f = v_i$, which implies that $v_f - v_i = 0$.
So $a = \frac{0 \frac{\text{m}}{\text{s}}}{t_f-t_i} = 0$
The question at the end of the problem usually tells us what the unknown is.
This problem is in the topic of 1-D Motion, or Kinematic Equations. There are only 3 equations relating to this topic; one equation relates our givens and unknown.
The first two equations contains the unknown, $t$.
So we can ignore the third equation for this problem.
Now, how do we choose between the remaining two equations? Well, the second equation contains the other given variables, the displacement ($s$), and the initial speed, $v_i$.
Believe it or not, at this point the problem is pretty much solved. A little bit of Algebra 1 is all that remains. There are a couple of different ways this can be done...
If you are uncomfortable manipulating an equation without all the numbers, you should probably substitute first. Rewrite the equation and "plug in" the values that were given. Then solve, probably using a calculator quite a bit. (Note that the units are all SI units, so they should work out.)
$$s = v_i t + \frac 1 2 a t^2$$
$$530 = 3.2 \times t + \frac 1 2 0 t^2$$
$$530 / 3.2 = t$$
$$t = 530 / 3.2 \text{s}$$
If you can handle it, consider solving the symbolic equation before plugging in the numbers or grabbing a calculator. Since there are only a few equations and a few variables, there can only be a relatively small number of unique problems. Solving symbolically and then plugging in the givens is a good way to start noticing that, and also reduces your calculator usage. Here, since we have an equation that is quadratic in $t$ (that is, the variable we are solving for has a $t^2$ term in the equation), we can do one of two things at this point.
(1) We can get the general solution for $t$ by using the quadratic formula
(2) We can notice that the quadratic term (that is, the $t^2$ term) will be zero because it is multiplied by a zero acceleration. For now, we will choose this second option, but we will show you the general solution in a later problem.
$$s = v_i t + \frac 1 2 a t^2$$$$s = v_i t + \frac 1 2 0 t^2$$$$s = v_i t$$$$\frac{s}{v_i} = t$$$$t = \frac{s}{v_i}$$$$t = \frac{530 \text{m}}{3.2 \frac{\text{m}}{\text{s}}}$$$$t = 530 / 3.2 \text{s}$$$$t = 166 \text{s}$$