A bus starting from rest is rolling down a hill with constant acceleration. If it travels a distance of 500 m in 25 seconds. Find the acceleration of the bus and the force acting on it. Consider the mass of the bus 5 metric tonnes.
Question
A bus starting from rest is rolling down a hill with constant acceleration. If it travels a distance of 500 m in 25 seconds. Find the acceleration of the bus and the force acting on it. Consider the mass of the bus 5 metric tonnes.
Solution
Sure, let's solve this step by step.
Step 1: Find the acceleration
We can use the equation of motion: s = ut + 0.5at^2
Where: s = distance = 500 m u = initial velocity = 0 (since the bus starts from rest) t = time = 25 seconds a = acceleration (which we are trying to find)
Substituting the values into the equation, we get:
500 = 025 + 0.5a*(25^2)
Solving for a, we get:
a = (500*2) / (25^2) = 1.6 m/s^2
So, the acceleration of the bus is 1.6 m/s^2.
Step 2: Find the force
We can use Newton's second law of motion: F = ma
Where: F = force m = mass = 5 metric tonnes = 5000 kg (since 1 metric tonne = 1000 kg) a = acceleration = 1.6 m/s^2
Substituting the values into the equation, we get:
F = 5000 * 1.6 = 8000 N
So, the force acting on the bus is 8000 N.
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