A train, with an initial velocity of 35ms^-1 along a straight track, deccelerates at a constant 0.25ms^2. Determine how far it travels in 2 minutes.
s(t) = vt + 1/2 at^2
so, using your numbers, with 2 minutes = 120 seconds,
s(120) = 35*120 - 1/2 * 1/4 * 120^2 = 2400m
Thank you!
To determine how far the train travels in 2 minutes, we need to use the equations of motion. The equation that relates displacement (distance traveled), initial velocity, acceleration, and time is given by:
s = ut + (1/2)at^2
where:
s - displacement (distance traveled)
u - initial velocity
a - acceleration
t - time
In this case, we are given:
u = 35 m/s (initial velocity)
a = -0.25 m/s^2 (deceleration, negative because it opposes motion)
t = 2 minutes
First, we need to convert the time from minutes to seconds because our units for velocity and acceleration are in meters per second and seconds, respectively. Therefore, 2 minutes is equal to:
t = 2 minutes × 60 seconds/minute
t = 120 seconds
Now we can substitute the values into the equation:
s = ut + (1/2)at^2
s = (35 m/s)(120 s) + (1/2)(-0.25 m/s^2)(120 s)^2
Calculating this equation will give us the distance traveled by the train in 2 minutes.