The position of a particle is described by the function x=2.5t^2 + -1.6t +2.8 (m). Determine the instantaneous velocity (in m/s) for the time t= 5.0s
To determine the instantaneous velocity at a specific time, we need to find the derivative of the position function with respect to time and then evaluate it at the given time.
Given the position function:
x = 2.5t^2 - 1.6t + 2.8 (m)
To find the derivative, we can use the power rule for differentiation:
For any term of the form cx^n, the derivative is given by:
d/dt(cx^n) = ncx^(n-1)
Taking the derivative of each term, we get:
dx/dt = d/dt(2.5t^2) - d/dt(1.6t) + d/dt(2.8)
= 5t - 1.6
Now, we can evaluate the derivative at the given time t = 5.0s:
v = dx/dt |t=5.0
= 5(5.0) - 1.6
= 25.0 - 1.6
= 23.4 m/s
Therefore, the instantaneous velocity at t = 5.0s is 23.4 m/s.