Final answer:
The train's deceleration when it hits the brakes at a speed of 70 m/s and takes 1 minute 55 seconds to stop is -0.61 m/s².
Step-by-step explanation:
To calculate the train's deceleration when going from 70 m/s to a stop in 1 minute 55 seconds, we need to use the formula for acceleration, which is a = ∆v / ∆t, where ∆v is the change in velocity and ∆t is the change in time. The initial velocity (v_i) is 70 m/s and the final velocity (v_f) is 0 m/s since the train comes to a stop. The time it takes to stop is 1 minute and 55 seconds, which we convert to seconds: 1 minute is 60 seconds plus 55 seconds equals 115 seconds total (∆t). Now using the formula: ∆v = v_f - v_i = 0 m/s - 70 m/s = -70 m/s (the negative sign indicates deceleration) ∆t = 115 s. Plugging these numbers into the acceleration formula: a = ∆v / ∆t = -70 m/s / 115 s. a = -0.61 m/s² (two decimal places). The negative sign here indicates that this is indeed a deceleration, so the train's acceleration is -0.61 m/s².