The position of an object is described as x = 4.0t and y= 1.5t2 - 2t + 1.0.
All factors are in SI-units.
a) What is the begining velocity of the object?
b) What is his acceleration?
c) What is the direction along the x-axe at the time t=1.0 s ?
Given answers are: 4.5 m/s in -27 degree; (0; 3.0 m/s2); +14 degree
Can someone please explain for me how to calculate these questions? I have no idea how to get these answers.
Sure! I can help you understand how to calculate these questions.
a) To find the initial velocity of the object, you need to calculate the derivative of the position function with respect to time (t).
The given position function is x = 4.0t. Taking the derivative of x with respect to t gives us the velocity function dx/dt.
dx/dt = d(4.0t)/dt = 4.0
Therefore, the initial velocity of the object is 4.0 m/s.
b) To find the acceleration of the object, you need to calculate the derivative of the velocity function with respect to time.
The velocity function is dx/dt = 4.0. Taking the derivative of dx/dt with respect to t gives us the acceleration function d2x/dt2.
d2x/dt2 = d(4.0)/dt = 0
Therefore, the acceleration of the object is 0 m/s².
c) To find the direction along the x-axis at the time t = 1.0 s, you need to calculate the derivative of the position function with respect to t, and then find the arctan of the resulting slope.
The given position function is x = 4.0t. Taking the derivative of x with respect to t gives us the slope of the position function, which is the tangent of the angle with the positive x-axis.
dx/dt = d(4.0t)/dt = 4.0
At t = 1.0 s, the slope is 4.0. To find the direction, we can calculate the angle using the arctan function:
angle = arctan(slope)
= arctan(4.0)
Using a calculator, we find that the angle is approximately 75.96 degrees.
Since the answer given is +14 degrees, it seems there might be an error in the calculation or the given answer.
To summarize:
a) The initial velocity of the object is 4.0 m/s.
b) The acceleration of the object is 0 m/s².
c) The direction along the x-axis at t = 1.0 s is approximately 75.96 degrees.