A particle moves in a linear motion according to: s = 10 - 6t2. Find the acceleration of the particle at t = 4s.
acceleration in m/s2 =
My Answer
s'= 0-12t
s"= -12
acceleration in m/s2 = -12
To find the acceleration of the particle at a specific time, you need to take the second derivative of the position function with respect to time. In this case, the position function is given as s = 10 - 6t^2.
First, take the first derivative of the position function to find the velocity function:
s' = d/dt(10 - 6t^2)
s' = 0 - 12t
s' = -12t
Next, take the second derivative of the position function to find the acceleration function:
s" = d/dt(-12t)
s" = -12
So, the acceleration of the particle at any given time t is -12 m/s^2.
Now, to find the acceleration at t = 4s, simply substitute t = 4 into the acceleration function:
s" = -12 (substituting t = 4)
acceleration at t = 4s = -12 m/s^2
Therefore, the acceleration of the particle at t = 4s is -12 m/s^2.