Final answer:
The train's acceleration is -0.777... m/s² when it hits the brakes at 70m/s and takes 1.5 minutes to stop.
Step-by-step explanation:
To calculate the train's acceleration when a train going 70m/s hits the brakes and takes 1.5 minutes to stop, we will use the formula for acceleration:
acceleration (a) = change in velocity (Δv) / time (t)
Firstly, we need to convert the time from minutes to seconds. Since 1 minute is equivalent to 60 seconds, 1.5 minutes is 1.5 × 60 = 90 seconds.
Since the train comes to a stop, the final velocity (vf) is 0 m/s and the initial velocity (vi) is 70 m/s. Therefore, the change in velocity (Δv) is vf - vi = 0 - 70 m/s = -70 m/s. Negative because the train is decelerating.
Using the formula for acceleration, we get:
a = Δv / t = -70 m/s / 90 s = -0.777… m/s²
The negative sign in the acceleration value indicates that the train is slowing down, which is expected since the train is decelerating, or experiencing a negative acceleration.
So, the train's acceleration is -0.777… m/s².