Question

Honda claims that its new super civic sports car will accelerate uniformly from rest to a speed of 87m/s in 8.0 seconds. A) determine the acceleration B) find the distance the car travels in the first 8 seconds.

Answer 1

Answer on Question #47734, Physics, Mechanics | Kinematics | Dynamics

Honda claims that its new super civic sports car will accelerate uniformly from rest to a speed of 87m/s in 8.0 seconds.

A) determine the acceleration

B) find the distance the car travels in the first 8 seconds.

Solution:

Given:

$$\begin{array}{l} v_{i} = 0 \mathrm{m/s}, \\ v_{f} = 87 \mathrm{m/s}, \\ t = 8 \mathrm{s}, \\ a = ?, \\ d = ? \end{array}$$

The kinematic equation that describes an object's motion is:

$$v_{f}^{2} = v_{i}^{2} + 2 a d$$

The symbol $d$ stands for the displacement of the object. The symbol $a$ stands for the acceleration of the object. And the symbol $v$ stands for the velocity of the object; a subscript of $i$ after the $v$ indicates that the velocity value is the initial velocity value and a subscript of $f$ indicates that the velocity value is the final velocity value.

The acceleration is

$$a = \frac{v_{f} - v_{i}}{t} = \frac{87 - 0}{8} = 10.875 \mathrm{m/s}^{2}$$ $$d = \frac{v_{f}^{2} - v_{i}^{2}}{2a} = \frac{87^{2}}{2 \cdot 10.875} = 348 \mathrm{m}$$

Answer: $a = 10.875 \mathrm{m/s}^{2}$,

$$d = 348 \mathrm{m}.$$

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