A rocket traveling at 165 m/s is accelerated at a rate of -32.0 m/s.
a) How long will it take before the instantaneous speed is 0 m/s? It takes 5.156 s.
b) How far will it travel during this time?
I will be happy to critique your thinking on this.
acceleration = -32.0 m/s
vf = 165 m/s
vi = 0
d = ?
Vf^2 = Vi^2 + 2ad
d = Vf^2 - Vf^2/2a
Yes, but the last line has a typo.
the second Vf is Vi
d = 165^2/(2 x 32.0)
d = 425.390
To find the time it takes for the instantaneous speed of the rocket to reach 0 m/s, we can use the equation:
Final velocity (Vf) = Initial velocity (Vi) + (Acceleration (a) × time (t))
Given that the initial velocity (Vi) is 165 m/s, the acceleration (a) is -32.0 m/s^2, and the final velocity (Vf) is 0 m/s, we can rearrange the equation to solve for time (t):
t = (Vf - Vi) / a
t = (0 - 165) / -32.0
Now, let's calculate the time it takes:
t = -165 / -32.0
t ≈ 5.156 seconds
Therefore, it will take approximately 5.156 seconds for the instantaneous speed of the rocket to reach 0 m/s.
To find the distance traveled during this time, we can use the equation:
Distance (d) = Initial velocity (Vi) × time (t) + (1/2) × acceleration (a) × time^2 (t^2)
Given that the initial velocity (Vi) is 165 m/s, the acceleration (a) is -32.0 m/s^2, and the time (t) is 5.156 seconds, we can calculate the distance:
d = 165 × 5.156 + (1/2) × (-32.0) × (5.156)^2
Now, let's calculate the distance:
d = 849.54 + (-25.55) × 26.58
d ≈ 849.54 + (-679.979)
d ≈ 169.56 meters
Therefore, the rocket will travel approximately 169.56 meters during the time it takes for the instantaneous speed to reach 0 m/s.