Question

1. NASA launches the Perseverance on its journey to Mars.  If the rocket is moving with a constant acceleration of 105 m/s2, how long will it take to travel 7400 m?

Formula:  x = x0 + v0t + ½ at2 

1. A person riding Nitro at Six Flags experiences an acceleration of 5.6 m/s2. As a result, it accelerates from rest to 37.4 m/s. How much distance did the person travel during that acceleration?

Formula: v2 = 2ax

1. An object accelerates from rest to a speed of 27 m/s over a distance of 62 m. What acceleration did it experience?

Formula: v2 = 2ax

1. An object accelerates from rest with a constant acceleration of 9.5 m/s2. How fast will it be traveling after it goes 25 m?

Formula: v2 = 2ax

Answer 1

1. From the formula, find the time (the acceleration is 105 m/s², the distance is 7400 m):

$$t=\sqrt\dfrac{2x}{a}=11.9\text{ s}.$$

2. The distance of the person:

$$x=\dfrac {v^2}{2a}=125\text{ m}.$$

3. The acceleration:

$$a=\dfrac{v^2}{2x}=5.88\text{ m/s}^2.$$

4. The speed:

$$v=\sqrt{2ax}=21.8\text{ m/s}.$$