A body moving with uniform acceleration travels 84m in the first 6seco...
Problem: A body moving with uniform acceleration travels 84m in the first 6 seconds and 180m in the next 5 seconds. Find the initial velocity and acceleration of the body.
Solution:
Step 1: Identify known values
We are given the following values:
- Distance covered in the first 6 seconds (s1) = 84m
- Distance covered in the next 5 seconds (s2) = 180m
- Total time taken (t) = 6 + 5 = 11 seconds
Step 2: Calculate acceleration
We can use the equation: Distance = Initial velocity x time + 1/2 x acceleration x time^2
For the first 6 seconds, we have:
84 = u x 6 + 1/2 x a x (6)^2
Simplifying the equation, we get:
36u + 108a = 84
For the next 5 seconds, we have:
180 = u x 5 + 1/2 x a x (5)^2
Simplifying the equation, we get:
25u + 25a = 36
Solving the above two equations simultaneously, we get:
Initial velocity (u) = 12 m/s
Acceleration (a) = 2 m/s^2
Step 3: Verify the solution
We can verify the solution by using the equations of motion:
v = u + at
s = ut + 1/2 at^2
For the first 6 seconds, we have:
v = 12 + 2 x 6 = 24 m/s
s = 12 x 6 + 1/2 x 2 x (6)^2 = 84 m (matches the given value)
For the next 5 seconds, we have:
v = 24 + 2 x 5 = 34 m/s
s = 24 x 5 + 1/2 x 2 x (5)^2 = 180 m (matches the given value)
Therefore, the initial velocity of the body is 12 m/s and the acceleration is 2 m/s^2.
A body moving with uniform acceleration travels 84m in the first 6seco...
Initial velocity= 84/6=14 m/s
Final velocity=180/5= 36m/s
Acceleration=36-14/11-6=22/5 m/s^2
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