Answer: His acceleration is -18.66m/s^2
Step-by-step explanation:
Ok, the initial speed is 2.8m/s. (we can define the initial direction as the positive direction).
And he wants to stop, so he must accelerate in the opposite direction as the initial movement, then we would have:
a(t) = -A.
So we have a constant, and negative acceleration.
Now, if we want to find the velocity we must integrate over time, and we will get:
v(t) = -A*t + V0
where V0 is the initial velocity, we know that it is 2.8m/s, and t is the time in seconds.
Then the velocity is:
v(t) = -A*t + 2.8m/s.
Now we know that John is brought to rest in 0.15 seconds after he starts slowing down, this means that at t = 0.15 seconds, his velocity is equal to zero.
v(0.15s) = 0m/s = -A*0.15s + 2.8m/s
2.8m/s = A*0.15s
2.8m/s/0.15s = 18.66m/s^2 = A.
So his acceleration is -A, then we have that:
His acceleration is -18.66m/s^2