An object\'s position y is given as y = At^2 + Bt + C, where A, B, and C are con
ID: 2166539 • Letter: A
Question
An object's position y is given as y = At^2 + Bt + C, where A, B, and C are constant and t is time.If A is a negative number and B is a positive number, which of the following correctly describe the motion?
a. the object initially moves in the negative direction, and slows down until it stop. Once it stops, it doesn't move again.
b. The object initially moves in the positive direction, slows down, and eventually turns around and starts moving in the negative direction.
c. The object initially moves in the negative direction, and slows down, and eventually turns around and starts moving in the positive direction.
Please explain why in your answer. (Correct Answer + Explanation = 5 stars)
Explanation / Answer
y = At2 + bt + C
velocity = dx/dt = 2At + b
Acceleration : dv/dt = 2A
Acceleration is negative as A is negative. Its velocity initially would be positive.
Hence,
b. The object initially moves in the positive direction, slows down, and eventually turns around and starts moving in the negative direction.