Question

A spacecraft is traveling in space at a velocity of 8200 m's. Turning a dial elicits the engines to accelerate the spacecraft at 2 m/s. How many seconds will it take

before the spacecraft reaches a velocity of 8400 m's?

Answer 1

It will take the spacecraft 100 seconds to increase its velocity from 8200 m/s to 8400 m/s when accelerating at 2 m/s² using the kinematic equation v = vo + at.

Step-by-step explanation:

To determine how many seconds it will take for a spacecraft traveling at a velocity of 8200 m/s to reach a velocity of 8400 m/s when accelerating at 2 m/s², we can use the kinematic equation for uniformly accelerated motion:

v = vo + at, where v is the final velocity, vo is the initial velocity, a is the acceleration, and t is the time.

Here, the initial velocity vo is 8200 m/s, the final velocity v is 8400 m/s, and the acceleration a is 2 m/s².

Plugging these values into the equation gives us:

8400 m/s = 8200 m/s + (2 m/s² × t)

To solve for t, we subtract 8200 m/s from both sides and then divide by the acceleration:

t = (8400 m/s - 8200 m/s) / (2 m/s²)

t = (200 m/s) / (2 m/s²)

t = 100 seconds

Therefore, it will take the spacecraft 100 seconds to increase its velocity from 8200 m/s to 8400 m/s.