Question

a bat is sitting in a tree. he leaves the tree and flies up to a speed of 4 meters per second in 8 seconds. how far does he travel? your car gets a flat! you go from 90 kilometers per hour to a stop in 6 seconds. what is your rate of deceleration? (its negative!) you skip north for 12 minutes to your best friends house that is 1.5 kilometers away. what is your average velocity? a fire truck is responding to an emergency. it accelerates from 0 to 66 km/hr in 11 seconds. what is its rate of acceleration? a space shuttle travels around the earth at a constant speed of 28000 kilometers per hour. if it takes 90 minutes to complete one orbit, how far is its journey around earth?

Explanation:

Step1: Recall distance - speed - time formula

The formula for distance $d$ is $d = v\times t$, where $v$ is speed and $t$ is time. For the bat, $v = 4$ m/s and $t=8$ s. So $d = 4\times8$.

Step2: Calculate the distance

$d=32$ m.

Step3: Recall acceleration formula

The formula for acceleration $a=\frac{v - u}{t}$, where $v$ is final velocity, $u$ is initial velocity and $t$ is time. For the car, $u = 90$ km/h. First convert 90 km/h to m/s: $90\times\frac{1000}{3600}=25$ m/s, $v = 0$ m/s, $t = 6$ s. Then $a=\frac{0 - 25}{6}=-\frac{25}{6}\approx - 4.17$ m/s².

Step4: Recall average - velocity formula

The formula for average velocity $v_{avg}=\frac{\Delta x}{\Delta t}$, where $\Delta x$ is displacement and $\Delta t$ is time. For the trip to the friend's house, $\Delta x=1.5$ km = 1500 m, $\Delta t = 12$ min = $12\times60 = 720$ s. So $v_{avg}=\frac{1500}{720}=\frac{25}{12}\approx2.08$ m/s north.

Step5: Recall acceleration formula for fire - truck

For the fire - truck, $u = 0$ km/h, $v = 66$ km/h. Convert 66 km/h to m/s: $66\times\frac{1000}{3600}=\frac{660}{36}=\frac{55}{3}$ m/s, $t = 11$ s. Then $a=\frac{\frac{55}{3}-0}{11}=\frac{5}{3}\approx1.67$ m/s².

Step6: Recall distance - speed - time formula for space - shuttle

For the space - shuttle, $v = 28000$ km/h, $t = 90$ min=$\frac{90}{60}=1.5$ h. Then $d=v\times t=28000\times1.5 = 42000$ km.

Answer:

1. The bat travels 32 m.
2. The car's deceleration is approximately $-4.17$ m/s².
3. The average velocity to the friend's house is approximately 2.08 m/s north.
4. The fire - truck's acceleration is approximately 1.67 m/s².
5. The space - shuttle's journey around the Earth is 42000 km.