Superman is flying 54.5m/s when he sees a train about to fall into a river 850m away. He must reach the train in 4.22s. What acceleration does he need?

Question

1-d kinematics question

Answer 1

You know that Superman’s initial speed is 54.5 m/s.

He only has 4.22 s to cover a distance of 850 m.

Assuming that Superman will have a constant acceleration to save the train, we can use the kinematic equations for constant acceleration. There are four of these:

1. d = v_i*t + 0.5*a*t²
2. v_f² = v_i² + 2*a*d
3. v_f = v_i + a*t
4. d = 0.5*t*(v_i + v_f)

Where d is distance, t is time, v_f is final velocity, v_i is initial velocity, and a is acceleration.

Since we know d, t, and v_i, and we want to find a, it would be best to avoid equations that involve variables other than these four. That means we should not use equations 2, 3, or 4. So we will use equation one, and solve for acceleration, so equation one becomes:

d = v_i*t + 0.5*a*t² ==> a = (d - v_i*t) / (0.5*t²)

Then we can plug in the numbers from the problem:

a = [850m - (54.5m/s * 4.22s)] / [0.5*(4.22s)²] = 69.6 m/s²

So Superman will have to accelerate at 70 m/s² to reach the train on time.