suppose a polar bear running with an initial speed of 4.0 m/s accelerates uniformly for 18s. what is the bear's maximum speed if the bear travels 135m during the 18s of acceleration? Give the answer in both meters per second and kilometers per hour.
distane=vi*time+ 1/2 aT^2
distance=4*18+ a*18^2 solve for a.
Then..
Vf=Vi + a*t
Well, well, well, we have a speedy polar bear here! Let's break it down. The bear starts at an initial speed of 4.0 m/s and accelerates uniformly for 18 seconds. During this time, it manages to cover a distance of 135 meters.
To find the maximum speed, we can use the formula for uniform acceleration:
v = u + at,
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Now, we know that the initial velocity (u) is 4.0 m/s, the time (t) is 18 seconds, and the distance covered (s) is 135 meters.
To find the acceleration (a), we can use the equation:
s = ut + (1/2)at^2.
Plugging in the values:
135 = (4.0)(18) + (1/2)(a)(18)^2.
Solving for a, we get:
a = 2(135 - 72)/18^2.
Calculating the value of a, we find:
a ≈ 0.185 m/s^2.
Now that we have the acceleration, we can find the final velocity (v) using our first equation:
v = 4.0 + (0.185)(18).
Calculating the value of v, we get:
v ≈ 7.33 m/s.
Fantastic! So the polar bear's maximum speed is approximately 7.33 m/s. Let's convert that into kilometers per hour to appreciate the bear's running skills:
1 meter per second is equivalent to approximately 3.6 kilometers per hour.
So, the bear's maximum speed is approximately:
7.33 m/s × 3.6 ≈ 26.4 km/h.
There you have it! Our fastest polar bear friend is zooming around at a maximum speed of approximately 7.33 m/s (or 26.4 km/h). Keep up the speedy work, polar bear! 🐻💨
To find the bear's maximum speed, we need to use the equation of uniformly accelerated motion:
v = u + at
where:
v = final velocity (maximum speed)
u = initial velocity (4.0 m/s)
a = acceleration (unknown)
t = time (18 s)
We also have the equation for displacement:
s = ut + 0.5at^2
where:
s = displacement (135 m)
u = initial velocity (4.0 m/s)
a = acceleration (unknown)
t = time (18 s)
Let's use the displacement equation to find the acceleration a:
s = ut + 0.5at^2
135 = 4(18) + 0.5a(18^2)
135 = 72 + 162a
162a = 135 - 72
162a = 63
a = 63 / 162
a ≈ 0.389 m/s^2
Now that we have the acceleration, we can use the velocity equation to find the bear's maximum speed:
v = u + at
v = 4.0 + (0.389)(18)
v ≈ 11.0 m/s
To convert the maximum speed to kilometers per hour (km/h), we can use the conversion factor:
1 m/s = 3.6 km/h
So the bear's maximum speed is approximately:
11.0 m/s * 3.6 km/h = 39.6 km/h
Therefore, the bear's maximum speed is approximately 11.0 m/s or 39.6 km/h.
To determine the maximum speed of the polar bear, we can use the equation for uniformly accelerated motion:
v_f = v_0 + at
Where:
v_f is the final velocity (maximum speed)
v_0 is the initial velocity (4.0 m/s)
a is the acceleration (which we need to calculate)
t is the time period (18s)
To find the acceleration, we can use the equation:
s = v_0t + (1/2)at^2
Where:
s is the displacement (135m)
Substituting the known values into the equation, we get:
135 = (4.0)(18) + (1/2)(a)(18^2)
Simplifying:
135 = 72 + 9a
Rearranging the equation to isolate the acceleration:
9a = 135 - 72
9a = 63
a = 63/9
a = 7 m/s^2
Now that we have the acceleration, we can substitute it back into the first equation to find the final velocity (maximum speed):
v_f = 4.0 + (7)(18)
v_f = 4.0 + 126
v_f = 130.0 m/s
To convert the answer to kilometers per hour, we can use the conversion factor 1 m/s = 3.6 km/h:
130.0 m/s * 3.6 km/h = 468 km/h
Therefore, the polar bear's maximum speed is 130.0 m/s or 468 km/h.