A body starts with an initial velocity of 10m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50 m/s the acceleration is reversed in direction without changing magnitude. Find the velocity of the particle when it reaches the starting point.
-70m/s^2
To find the velocity of the particle when it reaches the starting point, we need to break down the problem into two parts: the first part, where the particle accelerates from an initial velocity of 10 m/s to 50 m/s, and the second part, where the particle decelerates from 50 m/s back to the starting point.
Let's solve each part separately:
1. Acceleration from 10 m/s to 50 m/s:
In this part, the acceleration is in the same direction as the initial velocity. Let's denote the acceleration as "a".
Using the equation of motion v = u + at, where:
v = final velocity (50 m/s),
u = initial velocity (10 m/s),
a = acceleration (unknown),
t = time taken (unknown).
We can rearrange the equation to solve for "a":
50 = 10 + a * t
2. Deceleration from 50 m/s to the starting point:
In this part, the acceleration is in the opposite direction to the initial velocity. The magnitude of the acceleration remains the same. Let's denote the acceleration as "-a" (negative because it's in the opposite direction).
Using the same equation of motion, but now the final velocity is 0 m/s (since it's back to the starting point):
0 = 50 + (-a) * t'
We want to find the time taken during the deceleration phase, denoted as "t'".
Now, let's solve these two equations simultaneously to find the values of "a" and "t".
From the first equation, solving for "t":
t = (50 - 10) / a
t = 40 / a
Substituting this value of "t" into the second equation:
0 = 50 - a * (40 / a)
Simplifying the equation:
0 = 50 - 40
10 = a
We have found the value of "a" to be 10 m/s².
Now, let's go back to the first equation and substitute the value of "a":
50 = 10 + 10 * t
Solving for "t":
t = (50 - 10) / 10
t = 4 seconds
This means the acceleration phase lasted for 4 seconds.
Finally, to find the velocity of the particle when it reaches the starting point, we need to calculate the time taken during the deceleration phase, denoted as "t'".
Using the equation of motion for the deceleration phase:
0 = 50 + (-10) * t'
Solving for "t'":
t' = -50 / (-10)
t' = 5 seconds
The deceleration phase lasted for 5 seconds.
Now, let's find the velocity of the particle at the starting point using the equation of motion:
v = u + at
v = 50 + (-10) * 5
v = 50 - 50
v = 0 m/s
Therefore, the velocity of the particle when it reaches the starting point is 0 m/s.
To find the velocity of the particle when it reaches the starting point, we can use the concept of kinematics.
Step 1: Find the time taken for the velocity to change from 10 m/s to 50 m/s.
Given:
Initial velocity (u) = 10 m/s
Final velocity (v) = 50 m/s
Using the equation:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Rearranging the equation to solve for time (t), we get:
t = (v - u) / a
In this case, the acceleration (a) is constant.
Step 2: Find the time taken for the particle to reach the starting point once the acceleration is reversed.
To find this, we need to determine the time taken for the velocity to decrease from 50 m/s back to 0 m/s.
Given:
Initial velocity (u) = 50 m/s
Final velocity (v) = 0 m/s
Using the same equation as before (v = u + at) and rearranging to solve for time (t):
t = (v - u) / a
Step 3: Adding up the two times found in Step 1 and Step 2 will give us the total time taken for the particle to reach the starting point.
Step 4: Finally, we can find the velocity of the particle when it reaches the starting point by multiplying the total time by the magnitude of the acceleration and adding it to the initial velocity.
However, since the magnitude of the acceleration is not given in the question, we cannot determine the exact value of the velocity when the particle reaches the starting point without additional information.
position when it hits 50m/s:
vf^2=vi^2+2ad
50^2=10^2+2*a*d solve for a*d.
Now, the reverse trip:
vf^2=50^2 -2ad put the above in, and viola,
vf^2=50^2-50^2+10^2=10^2
vf=10
Think that out in your mind.