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Chapter 4: Problem 14

A subway train's mass is \(1.5 \times 10^{6} \mathrm{kg} .\) What force is required to accelerate the train at \(2.5 \mathrm{m} / \mathrm{s}^{2} ?\)

Short Answer

Expert verified
The force required to accelerate the train at \(2.5 m/s^{2}\) is \(3.75 \times 10^{6} N\).

Step by step solution

01

Identify given values

Identify the given values in the problem: the mass \(m\) of the subway train, which is \(1.5 \times 10^{6}\) kg, and the acceleration \(a\), which is \(2.5 m/s^{2}\).
02

Apply Newton's second law

Newton's second law of motion is defined as \(F = ma\), where \(F\) is the force, \(m\) is the mass, and \(a\) is the acceleration. We plug in the given values into this formula.
03

Compute the force

Multiply the mass of the train by the acceleration to find the force: \(F = 1.5 \times 10^{6} kg \times 2.5 m/s^{2} = 3.75 \times 10^{6} N\). Therefore, a force of \(3.75 \times 10^{6} N\) is required to accelerate the train at \(2.5 m/s^{2}\).

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