Final answer:
To find the distance covered by a rocket accelerating at 99.0 meters/second² to 445 meters/second over 4.50 seconds, we used the kinematic equation s = v_0 ⋅ t + ½ at², which yielded a result of approximately 1001.25 meters or 1.00 x 10³ meters in scientific notation. The correct answer is option B. 1.00 x 10³ meters.
Step-by-step explanation:
The student's question asks us to calculate the distance covered by a rocket accelerating at a rate of 99.0 meters/second² until it reaches a final velocity of 445 meters/second after accelerating for 4.50 seconds.
To solve this problem, we can use the kinematic equation for uniformly accelerated motion:
s = v_0 ⋅ t + ½ at²
Where:
s is the distance covered
v_0 is the initial velocity (which is 0 since the rocket starts at rest)
a is the acceleration
t is the time
Plugging the values into the equation, we get:
s = 0 ⋅ 4.50 s + ½ ⋅ 99.0 m/s² ⋅ (4.50 s)²
Calculating the covered distance:
s = 0 + ½ ⋅ 99.0 m/s² ⋅ 20.25 s²
s = ½ ⋅ 99.0 m/s² ⋅ 20.25 s²
s = 49.5 ⋅ 20.25 m
s = 1001.25 meters
Therefore, the nearest option to the distance covered by the rocket expressed in scientific notation is B. 1.00 x 10³ meters.