Answer :
Answer:
A) 2 m/s²
B) -12 m/s²
Explanation:
A)
- Applying the definition of instantaneous acceleration as the derivative of the velocity with respect to time, the acceleration vector can be expressed as follows:
- a = 2i^ + (-2t) j^ m/s²
- So, the x-component of the acceleration vector is constant, and equal to 2m/s², at any time.
- When t=6 s, aₓ= 2 m/s²
B)
- Applying the definition of instantaneous acceleration as the derivative of the velocity with respect to time, the acceleration vector can be expressed as follows:
- a = 2i^ + (-2t) j^ m/s²
- So, when t= 6s, the y component of a is as follows:
- ay = -2(6s) = -12 m/s²
A) The x-component of the particle's acceleration is; 2 m/s²
B) The y-component of the particle's acceleration at t = 6 is; -12 m/s²
X and Y components of Acceleration
We are given the velocity as;
v^ = 2t i^ + (3 − t²) j^ m/s
A) We know that acceleration is simply a derivative of velocity with respect to time. Thus;
a^ = dv/dt = 2 i^ + (-2t) j^ m/s²
The x - component of the acceleration is the figure attached to the vector i^.
Thus, x-component of acceleration = 2 m/s²
B) The y-component of the acceleration will be the value attached to the vector j^. Thus;
y-component of acceleration = -2t m/s²
At t = 6 s, we have;
y-component of acceleration = -2(6) = -12 m/s²
Read more about x and y components of acceleration at; https://brainly.com/question/7114558