Question

a rocket, initially at rest, steadily gains speed at a rate of 13.0m/s² for 6.90s during take - off. what was the rockets top speed? how far did the rocket travel during this time interval?

Explanation:

Step1: Find the top speed

Use the formula \(v = v_0+at\). Given \(v_0 = 0\ m/s\) (initially at rest), \(a=13.0\ m/s^{2}\), \(t = 6.90\ s\).

$$v=0 + 13.0\times6.90$$

$$v = 89.7\ m/s$$

Step2: Find the distance traveled

Use the formula \(s=v_0t+\frac{1}{2}at^{2}\). Since \(v_0 = 0\ m/s\), the formula simplifies to \(s=\frac{1}{2}at^{2}\).

$$s=\frac{1}{2}\times13.0\times(6.90)^{2}$$

$$s = 6.5\times47.61$$

$$s=309.465\ m$$

Answer:

Top - speed: \(89.7\ m/s\)
Distance: \(309.465\ m\)