(1) Calculate max velocity [tex]$30 m / s$[/tex]
(2) Acceleration in first 3 sec.
(2) Acceleration below 3 sec & 8 sec
3. [tex]$a=\frac{v-v}{t}$[/tex]
from 3 to 8
[tex]$0=30 m / s$[/tex]
[tex]$v=30 m / s$[/tex]
[tex]$x=\frac{30-30}{5}$[/tex]
From 8
[tex]$\mu=30 r$[/tex]
[tex]$v=0$[/tex]
[tex]$t=25$[/tex]
[tex]$a=$[/tex]
Answer (2)
Assuming the object starts from rest, calculate the acceleration in the first 3 seconds: a 1 ā = 3 30 ā 0 ā = 10 m / s 2 .
Calculate the acceleration between 3 and 8 seconds: a 2 ā = 5 30 ā 30 ā = 0 m / s 2 .
Calculate the acceleration from 8 seconds until the object stops: a 3 ā = 25 0 ā 30 ā = ā 1.2 m / s 2 .
The accelerations are a 1 ā = 10 m / s 2 , a 2 ā = 0 m / s 2 , and a 3 ā = ā 1.2 m / s 2 , respectively. a 1 ā = 10 s 2 m ā , a 2 ā = 0 s 2 m ā , a 3 ā = ā 1.2 s 2 m ā ā
Explanation
Problem Setup We are given the maximum velocity of an object as 30 m / s . We need to calculate the acceleration in the first 3 seconds, the acceleration between 3 and 8 seconds, and the acceleration after 8 seconds until the object stops. We will use the formula for acceleration, which is the change in velocity divided by the change in time: a = Ī t Ī v ā = t f ā ā t i ā v f ā ā v i ā ā , where v f ā is the final velocity, v i ā is the initial velocity, t f ā is the final time, and t i ā is the initial time.
Acceleration in the First 3 Seconds First, let's calculate the acceleration in the first 3 seconds. We are given that the final velocity at 3 seconds is 30 m / s . We need to assume an initial velocity to solve this. Let's assume the object starts from rest, so the initial velocity v i ā = 0 m / s . Then, the acceleration a 1 ā in the first 3 seconds is:
a 1 ā = 3 s ā 0 s 30 m / s ā 0 m / s ā = 3 30 ā m / s 2 = 10 m / s 2 .
Acceleration Between 3 and 8 Seconds Next, let's calculate the acceleration between 3 and 8 seconds. We are given that the velocity at 3 seconds is 30 m / s and the velocity at 8 seconds is 30 m / s . Therefore, the acceleration a 2 ā between 3 and 8 seconds is:
a 2 ā = 8 s ā 3 s 30 m / s ā 30 m / s ā = 5 0 ā m / s 2 = 0 m / s 2 .
Acceleration After 8 Seconds Finally, let's calculate the acceleration from 8 seconds until the object stops. We are given that the initial velocity at 8 seconds is 30 m / s and the object stops, so the final velocity is 0 m / s . The time taken to stop is 25 seconds. Therefore, the acceleration a 3 ā from 8 seconds until the object stops is:
a 3 ā = 25 s 0 m / s ā 30 m / s ā = 25 ā 30 ā m / s 2 = ā 1.2 m / s 2 .
Final Answer Therefore, the acceleration in the first 3 seconds is 10 m / s 2 , the acceleration between 3 and 8 seconds is 0 m / s 2 , and the acceleration after 8 seconds until the object stops is ā 1.2 m / s 2 .
Examples
Understanding acceleration is crucial in many real-world scenarios. For example, when designing a car, engineers need to calculate the acceleration and deceleration rates to ensure the safety and comfort of the passengers. Similarly, in sports, athletes use acceleration to improve their performance, such as sprinting or throwing a ball. Calculating acceleration helps in optimizing the design and performance of various systems and activities.
The acceleration during the first 3 seconds is 10 m/sĀ², between 3 and 8 seconds is 0 m/sĀ², and after 8 seconds until it stops is -1.2 m/sĀ². The calculations are based on the change in velocity over time intervals. This breakdown helps understand how acceleration varies in different phases of motion.
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