Question

a race car acceleration from 0 m/s to 30 m/s with a displacement of 45 m. what is the vehicle's acceleration ?

Answer 1

Answer on Question#37935- Physics – Other

A race car acceleration from $0\,\mathrm{m/s}$ to $30\,\mathrm{m/s}$ with a displacement of $45\,\mathrm{m}$ what is the vehicle's acceleration?

Solution:

The equation of motion for the car ($d = 45\,\mathrm{m}$):

$$x: d = \frac{a t^2}{2}$$

Rate equation for the car ($V = 30\,\frac{\mathrm{m}}{\mathrm{s}}$):

$$V = a t$$ $$t = \frac{V}{a}$$

(2)in(1):

$$d = \frac{a}{2} \cdot \left(\frac{V}{a}\right)^2 = \frac{V^2}{2a}$$ $$a = \frac{V^2}{2d} = \frac{\left(30\,\frac{\mathrm{m}}{\mathrm{s}}\right)^2}{2 \cdot 45\,\mathrm{m}} = 10\,\frac{\mathrm{m}}{\mathrm{s}^2}$$

Answer: acceleration of the car is equal to $10\,\frac{\mathrm{m}}{\mathrm{s}^2}$