Final answer:
To find the time t when the particle comes to rest, we set the given equation v = (27t - 18)² to zero and solve for t, finding that the particle comes to rest at t = 2/3 seconds.
Step-by-step explanation:
To solve for the time t at which the particle comes to rest, we know that rest implies a velocity v of 0 m/s. Given the velocity equation v = (27t - 18)², we set the equation equal to zero and solve for t.
0 = (27t - 18)²
To find the values of t, we take the square root of both sides:
- 0 = 27t - 18
- t = 18/27
- t = 2/3
Therefore, the time at which the particle comes to rest is t = 2/3 seconds.