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Ch 02: Kinematics in One Dimension
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 02: Kinematics in One DimensionProblema 13a
Capitolo 2, Problema 13a

What constant acceleration, in SI units, must a car have to go from zero to 60 mph in 10 s?

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1
Convert the speed from miles per hour (mph) to meters per second (m/s) using the conversion factor: 1 mph = 0.44704 m/s. Thus, 60 mph = 60 × 0.44704 m/s.
Write the kinematic equation for constant acceleration: a = \(\frac{v_f - v_i}{t}\), where v_f is the final velocity, v_i is the initial velocity, and t is the time.
Substitute the known values into the equation: v_i = 0 (since the car starts from rest), v_f (calculated in step 1), and t = 10 \; \(\text{s}\).
Simplify the equation to solve for a, the constant acceleration.
Express the result in SI units (m/s²), ensuring all calculations adhere to the proper unit conversions and significant figures.

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Acceleration

Acceleration is the rate of change of velocity of an object with respect to time. It is a vector quantity, meaning it has both magnitude and direction. In this context, constant acceleration refers to a uniform increase in speed, which can be calculated using the formula a = (v_f - v_i) / t, where v_f is the final velocity, v_i is the initial velocity, and t is the time taken.
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Percorso guidato
05:47
Intro to Acceleration

Conversion of Units

To solve the problem, it is essential to convert the speed from miles per hour (mph) to meters per second (m/s), as SI units are required. The conversion factor is 1 mph = 0.44704 m/s. Therefore, 60 mph can be converted to m/s by multiplying by this factor, which is crucial for accurately calculating the acceleration.
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Unit Conversions

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. One relevant equation is v_f = v_i + at, which relates final velocity, initial velocity, acceleration, and time. This equation can be rearranged to solve for acceleration when the initial and final velocities and the time interval are known, making it a key tool for solving the given problem.
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Kinematics Equations
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