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The standard (Bose–Einstein/Fermi–Dirac, or Maxwell–Boltzmann) distribution from the relativistic ideal gas model is used to study the transverse momentum (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>p</mi><mi>T</mi></msub></semantics></math></inline-formula>) spectra of identified charged hadrons (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>π</mi><mo>−</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>π</mi><mo>+</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>−</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>+</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></semantics></math></inline-formula>, and <i>p</i>) with different rapidities produced in inelastic proton–proton (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>p</mi></mrow></semantics></math></inline-formula>) collisions at a Super Proton Synchrotron (SPS). The experimental data measured using the NA61/SHINE Collaboration at the center-of-mass (c.m.) energies <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>6.3</mn></mrow></semantics></math></inline-formula>, 7.7, 8.8, 12.3, and 17.3 GeV are fitted well with the distribution. It is shown that the effective temperature (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub></semantics></math></inline-formula> or <i>T</i>), kinetic freeze-out temperature (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>0</mn></msub></semantics></math></inline-formula>), and initial temperature (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>i</mi></msub></semantics></math></inline-formula>) decrease with the increase in rapidity and increase with the increase in c.m. energy. The kinetic freeze-out volume (<i>V</i>) extracted from the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>π</mi><mo>−</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>π</mi><mo>+</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>−</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>+</mo></msup></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></semantics></math></inline-formula> spectra decreases with the rapidity and increase with the c.m. energy. The opposite tendency of <i>V</i>, extracted from the <i>p</i> spectra, is observed to be increasing with the rapidity and decreasing with the c.m. energy due to the effect of leading protons.