particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed when t = 6. (Round your answers to two decimal places.)
f(t) = t−1 − t
velocity m/s
speed m/s
To find the velocity, we need to find the derivative of the equation of motion with respect to time. The derivative of f(t) will give us the velocity function.
Given equation of motion: s = f(t) = t - 1 - t
To find the derivative, we will differentiate the equation with respect to t:
ds/dt = d/dt(t - 1 - t)
ds/dt = d/dt(-1)
ds/dt = 0
Since the derivative of a constant is zero, the velocity function is zero. Therefore, the velocity of the particle at any time t is 0 m/s.
Now, let's find the speed when t = 6.
To find the speed, we need to take the absolute value of the velocity. Since we found that the velocity is 0 m/s, the speed is also 0 m/s.
Therefore, the velocity is 0 m/s and the speed is 0 m/s when t = 6.