Question

A rocket is traveling in space with a constant velocity of 10 m/s when it fires up a booster. The booster accelerates the rocket at a rate of 5 m/s². What distance in meters has the rocket traveled within 12 seconds after the booster turned on?

Option 1: 60 meters
Option 2: 120 meters
Option 3: 180 meters
Option 4: 240 meters

Answer 1

The rocket travels 480 meters after 12 seconds once the booster is turned on, calculated using the equation S = Vo*t + ½*a*t² with the given initial velocity and acceleration values, which do not match the provided options.

Step-by-step explanation:

The question asks for the distance traveled by a rocket that starts at a constant velocity of 10 m/s and then accelerates at a rate of 5 m/s² after its booster is fired. To find the distance traveled, we need to use the kinematic equation for uniformly accelerated motion:

S = Vot + ½at²

Where:

• S is the distance traveled
• Vo is the initial velocity (10 m/s)
• a is the acceleration (5 m/s²)
• t is the time (12 seconds)

Plugging in the values we get:

S = (10 m/s)(12 s) + ½(5 m/s²)(12 s)²

S = 120 m + 30 m/s²(144 s²)

S = 120 m + 360 m

S = 480 m

However, none of the options provided in the question match the calculated distance. There might be a mistake in the question or the options given. The correct answer should be 480 meters.