michael starts at x=3 m and travels to the right at a constant 6 m/s for 2 s. he then slows down at a constant rate, coming to rest at 4 s after beginning to slow. A) what is michael's position when t=4 s.? C) What is Michael's velocity when t=4 s? d) What is Michael's acceleration when t=4 s?
To solve this problem, we need to break it down into parts and calculate Michael's position, velocity, and acceleration at different points in time.
Given:
Initial position (x₀) = 3 m
Constant velocity (v) = 6 m/s
Time taken to reach rest after slowing down (t₁) = 4 s
Step 1: Calculate Michael's position at t = 4 s (x₁).
We know that Michael travels at a constant velocity for 2 s, so we can calculate his position after 2 s using the formula:
x₁ = x₀ + v * t
x₁ = 3 + 6 * 2
x₁ = 3 + 12
x₁ = 15 m
Therefore, Michael's position at t = 4 s is 15 m.
Step 2: Calculate Michael's velocity at t = 4 s (v₁).
To find Michael's velocity at t = 4 s, we need to calculate the deceleration first.
Deceleration (a) = (Final velocity - Initial velocity) / Time
Since Michael comes to rest at t₁ = 4 s, his final velocity (v₁) will be 0 m/s.
a = (v₁ - v₀) / t₁
0 = (v₁ - 6) / 4
0 = v₁ - 6
v₁ = 6 m/s
Therefore, Michael's velocity at t = 4 s is 6 m/s.
Step 3: Calculate Michael's acceleration at t = 4 s (a₁).
To find Michael's acceleration at t = 4 s, we need to calculate the rate of deceleration, which is constant.
Acceleration (a) = (Final velocity - Initial velocity) / Time
a₁ = (0 - 6) / 4
a₁ = -6/4
a₁ = -1.5 m/s²
Therefore, Michael's acceleration at t = 4 s is -1.5 m/s².
In summary:
A) Michael's position when t = 4 s is 15 m.
B) Michael's velocity when t = 4 s is 6 m/s.
C) Michael's acceleration when t = 4 s is -1.5 m/s².