A particle travels along a straight line with a speed = (0.50 -7 ), where is in seconds. Determine the acceleration of the particle when = 2 .
To determine the acceleration of the particle when t = 2, we need to differentiate the given velocity function with respect to time, since acceleration is the rate of change of velocity with respect to time.
Given velocity v(t) = (0.50t - 7), we can differentiate it to find the acceleration function a(t) as follows:
a(t) = d(v(t))/dt
First, differentiate the first term:
d(0.50t)/dt = 0.50
Since the derivative of a constant (in this case, 7) is zero, we can drop the 7.
So, the acceleration function a(t) = 0.50.
Now, we can substitute t=2 into the acceleration function to find the acceleration at t=2.
a(2) = 0.50
Therefore, the acceleration of the particle when t=2 is 0.50.