Question

Тело, двигаясь из состояния покоя с ускорением 5 м/с2, достигло скорости 30 м/с, а затем, двигаясь равномедленно, остановилось через 10 с. определить путь, пройденный телом за все время движения

Answer 1

A=5 м/с²    v=30 м/с    t=10 c
===
s1=v²/(2*a)=900/(2*5)=90 м
s2=(v+0)*t/2=30*10/2=150 м
s=s1+s2=90+150=240 м
==========================

Answer 2

Calculation of the Distance Traveled by the Body

To calculate the distance traveled by the body, we need to consider the different stages of its motion.

1. Stage 1: Acceleration from rest to a velocity of 30 m/s

The body starts from rest and accelerates with an acceleration of 5 m/s^2 until it reaches a velocity of 30 m/s. We can use the equation of motion to calculate the time taken to reach this velocity:

   v = u + at
   30 = 0 + 5t
   t = 6 seconds
   

Now, we can calculate the distance covered during this stage using the equation of motion:

   s = ut + (1/2)at^2
   s = 0 + (1/2)(5)(6)^2
   s = 90 meters
   

2. Stage 2: Constant velocity motion

After reaching a velocity of 30 m/s, the body continues to move at a constant velocity for 10 seconds. Since the velocity is constant, the distance covered during this stage can be calculated using the formula:

   s = vt
   s = 30 * 10
   s = 300 meters
   

3. Stage 3: Deceleration to rest

Finally, the body decelerates and comes to rest over a period of 10 seconds. Since the body is decelerating, the acceleration is negative (-5 m/s^2). We can calculate the distance covered during this stage using the equation of motion:

   v = u + at
   0 = 30 + (-5)t
   t = 6 seconds
   

Now, we can calculate the distance covered during this stage using the equation of motion:

   s = ut + (1/2)at^2
   s = 30 * 6 + (1/2)(-5)(6)^2
   s = 180 - 90
   s = 90 meters
   

Total Distance Traveled

To find the total distance traveled by the body, we add up the distances covered in each stage:

Total distance = Distance in Stage 1 + Distance in Stage 2 + Distance in Stage 3
Total distance = 90 + 300 + 90
Total distance = 480 meters

Therefore, the body traveled a total distance of 480 meters during its entire motion.