Question

A train passes a point at some unknown velocity. It took the train 7.2 seconds to travel 100 meters further while accelerating at 0.23 m/s^2. What was the initial velocity? If the total time is 12 seconds.

a) 25 m/s
b) 20 m/s
c) 15 m/s
d) 10 m/s

Answer 1

The initial velocity of the train is found to be 10 m/s after applying the equations of motion with constant acceleration using the given data of 100 meters, 7.2 seconds, and 0.23 m/s^2 acceleration.

Step-by-step explanation:

To determine the initial velocity of the train, we can use the equations of motion for constant acceleration. Given that the total time to travel the additional 100 mete rs is 7.2 seconds and the acceleration is 0.23 m/s2, we can use the equation:

v = u + at

where:
v = final velocity (which we don't directly need),
u = initial velocity (which we are looking for),
a = acceleration = 0.23 m/s2,
t = time = 7.2 s.

The final position (s) after time t can be calculated using the equation:

s = ut + (1/2)at2

Substituting the known values and the additional information that s = 100 m, we can rearrange the equation to solve for the initial velocity (u):

100 m = u(7.2 s) + (1/2)(0.23 m/s2)(7.2 s)2

After calculating, we find that u = 10 m/s which matches option (d).