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Chapter 2: Problem 27

ThrustSSC, the world's first supersonic car, accelerates from rest to \(1000 \mathrm{km} / \mathrm{h}\) in \(16 \mathrm{s} .\) What's its acceleration?

Short Answer

Expert verified
The acceleration of the car is approximately \( 17.36 \, m/s^2 \).

Step by step solution

01

Convert Speed

The top speed is given in km/h, but the standard unit of acceleration, \( m/s^2 \), requires the speed in m/s. To convert from km/h to m/s, multiply by \( 1000/3600 = 0.27778 \). So, \( 1000 \, km/h = 1000 \times 0.27778 = 277.78 \, m/s \).
02

Apply Acceleration Formula

The formula of acceleration \( a \) is \( a = \Delta v / \Delta t \), where \( \Delta v \) is the change in velocity and \( \Delta t \) is the change in time. Since the car starts from rest, the initial speed is 0. Therefore, \( \Delta v = 277.78 - 0 = 277.78 \, m/s \). The time \( \Delta t \) is 16 seconds. Applying the values into the formula, it becomes \( a = 277.78 \, m/s / 16 \, s \).
03

Calculate Acceleration

By performing the calculation as described in the previous step, the acceleration \( a \) of the car comes out as \( a = 277.78 / 16 = 17.36 \, m/s^2 \).

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