A toy train leaves a station at time t=0.0 and moves with constant acceleration. If the total mass of the train is 5.5 kg and its acceleration is 9.9 m/s2. What is the total work done on the train after 1.1 s? Express your answer in kJ.
To find the total work done on the train, we need to use the work-energy principle.
The work done on an object is given by the formula:
Work = Force * Distance * cos(theta)
In this case, since the train is moving with constant acceleration, we can use the formula of work done for an object with constant acceleration:
Work = (0.5) * m * (v^2 - u^2)
Where:
m = mass of the train = 5.5 kg
v = final velocity of the train
u = initial velocity of the train
a = acceleration of the train = 9.9 m/s^2
t = time = 1.1 s
To find the final velocity of the train, we can use the equation of motion:
v = u + a * t
Substituting the given values, we have:
v = 0 + 9.9 * 1.1
v = 10.89 m/s
Now, we can calculate the work done:
Work = (0.5) * 5.5 * ((10.89^2) - (0^2))
Work ≈ 332.68 J
To convert this to kJ, we divide by 1000:
Work ≈ 0.33268 kJ
Therefore, the total work done on the train after 1.1 s is approximately 0.33268 kJ.