Question

John is gliding along on his scooter at a speed of 2.8 m/s when

suddenly he collides with Sam who is walking around the corner. If
John is brought to rest in 0.15 s, what is his acceleration?

Answer 1

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