the speed boat has a acceleration of 2.0 m/s2 if the initial velocity of the boat is 6.0 m/s2. find the boat displacement after 8.0 seconds?
1609/4.740
and
1609/4.695
x = 6 t + (1/2)(2) t^2
= 6(8) + 64
= 112 meters
car 1 travel from left to right and covers a distance of 1.609m(1mile) in a time of 4.740seconds. car 2 covers the same distance in 4.695seconds in the same direction. determine the average velocity for each car?
Well, if the boat is accelerating at 2.0 m/s² and the initial velocity is 6.0 m/s, that means the boat's velocity will increase by 2.0 m/s each second. After 8 seconds, the velocity would be 22.0 m/s.
Now, to find the displacement, we need to remember that displacement is the change in position. Since the boat is accelerating, we can't simply multiply the velocity by the time. We need to use the equation s = ut + 0.5at², where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Plugging in the numbers, we get s = (6.0 m/s)(8.0 s) + 0.5(2.0 m/s²)(8.0 s)².
After doing the math, we find that the boat's displacement after 8.0 seconds is 288 meters. It seems like the boat is on a speedy journey!
To find the displacement of the boat after 8.0 seconds, you can use the formula:
displacement = initial velocity × time + (1/2) × acceleration × time²
Given:
Initial velocity (u) = 6.0 m/s
Acceleration (a) = 2.0 m/s²
Time (t) = 8.0 s
Substituting the values:
displacement = (6.0 m/s) × (8.0 s) + (1/2) × (2.0 m/s²) × (8.0 s)²
Now, let's calculate it step by step:
1. Initial velocity × time:
= (6.0 m/s) × (8.0 s)
= 48.0 m
2. (1/2) × acceleration × time²:
= (1/2) × (2.0 m/s²) × (8.0 s)²
= (1/2) × (2.0 m/s²) × (64 s²)
= 64.0 m
Therefore,
displacement = 48.0 m + 64.0 m
displacement = 112.0 m
So, the boat's displacement after 8.0 seconds is 112.0 meters.