Answer:
Therefore, the magnitude of the acceleration of the particle at the instant when its velocity is zero is approximately 18.258 m/s².
Step-by-step explanation:
To find the magnitude of acceleration at the instant when velocity is zero, we need to differentiate the given velocity equation with respect to time (t) to obtain the acceleration equation.
Given:
Velocity equation: v(t) = 22 - 3.8t^2
Differentiating the velocity equation with respect to time, we get:
a(t) = d(v(t))/dt = -2 * 3.8t
To find the magnitude of acceleration at the instant when velocity is zero, we need to solve for t when v(t) = 0.
0 = 22 - 3.8t^2
3.8t^2 = 22
t^2 = 22/3.8
t^2 ≈ 5.789
Taking the square root of both sides, we find:
t ≈ √(5.789)
t ≈ 2.403
Now we can substitute this value of t into the acceleration equation to find the magnitude of acceleration at that instant:
a(t) = -2 * 3.8 * 2.403
a(t) ≈ -18.258
Therefore, the magnitude of the acceleration of the particle at the instant when its velocity is zero is approximately 18.258 m/s².