Question

Three students are discussing the motion of an object which is described by the following equation: x(t)= -4m -(9m/s)t + (2m/s^2)t^2

The students make the following contentions about the motion during the first 2 seconds: Amadeo: "I think this object's instantaneous speed will increase with time since the acceleration is positive.
Barrett: "No, the object will have a decreasing speed, since the acceleration is directed opposite to the initial velocity
Chinue: "I don't think we can tell what will happen to the speed from this equation, since it tells us about the position as a function of time, not about speed or velocity."
Which, if any, of these three students do you agree with?
A. Amadeo
B. Barrett
C. Chinue
E. None of them.

Answer 1

Barret True, the speed decreases with increasing time

Step-by-step explanation:

The equation they give us to describe the movement is of the form

y = yo + v₀ t + ½ a t²

The given equation is

y = -4 - 9 t + 2 t²

We can match term to term and find the constants

y₀ = -4 m

v₀ = -9 m / s

a = 2 m / s²

With this data we can build the equation of speed and time

v = v₀ + a t

v = - 9 + 2 t

With this expression we see that as time increases the speed decreases since the speed and acceleration have direction is opposite

Now we can analyze the students' observations

Amadeo False, we see that the behavior is the opposite

Barret True, the speed decreases with increasing time

Chinue False With the equation we have all the data to build the speed equation as a function of time