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

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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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.