Question

1. a helicopters speed increases from 25 m/s to 60 m/s in 5 seconds. what is the acceleration of this helicopter?
2. as she climbs a hill, a cyclist slows down from 25 mi/hr to 6 mi/hr in 10 seconds. what is her deceleration?
3. a motorcycle traveling at 25 m/s accelerates at a rate of 7 m/s² for 6 seconds. what is the final speed of the motorcycle?
4. a car starting from rest accelerates at a rate of 8 m/s². what is its final speed at the end of 4 seconds?
5. after traveling for 6 seconds, a runner reaches a speed of 10 m/s. if the runner started from rest, what is the runners acceleration?
6. a cyclist starts from rest and accelerates at a rate of 7 m/s². how long will it take the cyclist to reach a speed of 18 m/s?
7. a skateboarder traveling at 7 meters per second rolls to a stop at the top of a ramp in 3 seconds. what is the skateboarders acceleration?

Explanation:

Step1: Recall the acceleration formula

The formula for acceleration is \(a=\frac{v - u}{t}\), where \(v\) is the final velocity, \(u\) is the initial velocity, and \(t\) is the time.

Step2: Substitute the values for the helicopter

For the helicopter, \(u = 25\space m/s\), \(v=60\space m/s\), and \(t = 5\space s\).

$$a=\frac{60 - 25}{5}=\frac{35}{5}$$

Step3: Calculate the acceleration

$$a = 7\space m/s^{2}$$

Step1: Recall the deceleration formula

Deceleration \(a=\frac{v - u}{t}\), where \(v\) is the final velocity, \(u\) is the initial velocity, and \(t\) is the time.

Step2: Substitute the values for the cyclist

For the cyclist, \(u = 25\space mi/hr\), \(v = 6\space mi/hr\), and \(t=10\space s\). First, convert the velocities to \(m/s\) (but since we are calculating the rate of change, the units for velocity change will cancel out with time in seconds).

$$a=\frac{6 - 25}{10}=\frac{- 19}{10}$$

Step3: Calculate the deceleration

$$a=-1.9\space mi/hr - s$$

Step1: Recall the final - velocity formula

The formula for final velocity is \(v=u+at\), where \(u\) is the initial velocity, \(a\) is the acceleration, and \(t\) is the time.

Step2: Substitute the values for the motorcycle

For the motorcycle, \(u = 25\space m/s\), \(a = 7\space m/s^{2}\), and \(t = 6\space s\).

$$v=25+7\times6$$

Step3: Calculate the final velocity

$$v=25 + 42=67\space m/s$$

Step1: Recall the final - velocity formula

The formula for final velocity is \(v=u+at\), where \(u\) is the initial velocity, \(a\) is the acceleration, and \(t\) is the time. Since the car starts from rest, \(u = 0\space m/s\).

Step2: Substitute the values for the car

For the car, \(a = 8\space m/s^{2}\), \(t = 4\space s\), and \(u = 0\space m/s\).

$$v=0+8\times4$$

Step3: Calculate the final velocity

$$v = 32\space m/s$$

Answer:

The acceleration of the helicopter is \(7\space m/s^{2}\)