Looking through a high school physics textbook I saw the following problem:
“The velocity of a cart is to be measured by two lasers a distance apart. The cart starts at the first laser. At this point it is at rest so its speed is 0 m/s. It’s then pushed and passes through the second laser 5 seconds later. The lasers are linked to a computer which shows that the final velocity of the cart as it passes through the second laser is 2.0 m/s. Calculate the acceleration of the cart.”
Now, the textbook gives the following answer: 1 m/s[sup]2[/sup].
However, as I remember from my own high school physics lessons, the formula for calculating acceleration is v minus u divided by t, where v is the final velocity (in this case 2.0 m/s), u is the initial velocity (0 m/s), and t is time. 2 - 0 is 2, divided by 5 is 0.4, so the acceleration should be 0.4m/s[sup]2[/sup].
If the problem is as stated, and the cart is undergoing uniform acceleration the entire time (which is what I’d expect from a high-school physics textbook) then your answer is correct. Not sure what the textbook is on about; maybe someone changed the numbers in one of the problems between editions of the textbook (which is a common practice) but forgot to change the solutions.
You have just learned the single most important lesson to be learned in physics (or indeed, in any science): The textbook is not always right. In fact, I’d go so far as to say that “the textbook is not always right” is at the core of what science means.
The question does not sound right. Pushing the cart at a constant acceleration (constant force) seems improbable.
Is there someway that you missed out that a force was applied for the first 2 seconds (the push) and the cart slides from then on ? If so, the 1m/s2 seems to fit.
Some of the books I used would sometimes have answers, for example, for the odd numbered questions. I would check the texts to see if their answers were correct. Occasionally I would find one that was wrong. Of course I’d assign that one.
Almost all students of course would just parrot back the text’s answer. I would point out when covering the right answer that I’m not an idjit. I know there’s an answer in the book. Doesn’t it occur to the students that maybe I assigned it for a reason?
Maybe it’s not being pushed. For example, maybe the cart is on a hill so that gravity is doing the work. Ignoring friction (and a textbook would) this would give you a constant acceleration.
In any event, it sounds like a very similar problem back in my high school days that the textbook also got wrong.
My highschool experience was that calculus was taught a lot later than the statics or dynamics in Physics. Then you had relearn the use of calculus with physics. For example :
v = u + ft or f= (v-u)/t … taught in the 9th grade
Taught in the 11th grade
dv/dt = f (much simpler and elegant and good for linear motion)
Forgot which grade when understood:
dv/dt = f (vectors. much simpler and easy to use for circular and parabolic and all sorts of motion)
In my opinion - vectors and calculus should be taught first since it gets easier to visualize and solve
