A BODY MOVING WITH A UNIFORM ACCELERATION. IT TRAVELS 84M IN FIRST 6 SEC AND TRAVEL 180M IN 5 SEC FIND ITS INITIAL VELOCITY AND ACCELERETION
To find the initial velocity and acceleration of a body moving with uniform acceleration, we can use the following equations of motion:
1. Displacement (s) = Initial velocity (u) × Time (t) + (1/2) × Acceleration (a) × Time (t)^2
2. Final velocity (v) = Initial velocity (u) + Acceleration (a) × Time (t)
Let's solve the problem step by step:
Given data:
Displacement in the first 6 seconds (s1) = 84 m
Displacement in the next 5 seconds (s2) = 180 m
Time taken for s1 (t1) = 6 s
Time taken for s2 (t2) = 5 s
Step 1: Finding the acceleration (a)
Using the equation of motion (1) for s1:
s1 = u × t1 + (1/2) × a × t1^2
84 = u × 6 + (1/2) × a × 6^2
Simplifying the equation:
84 = 6u + 18a
Using the equation of motion (1) for s2:
s2 = u × t2 + (1/2) × a × t2^2
180 = u × 5 + (1/2) × a × 5^2
Simplifying the equation:
180 = 5u + 12.5a
Step 2: Solving the equations simultaneously
We now have two equations with two unknowns (u and a). We can solve these equations using any method such as substitution or elimination.
Let's use the elimination method to solve the equations:
Multiply the first equation by 5, and the second equation by 6 to make the coefficients of 'u' equal:
5(84) = 6(180)
Simplifying the equation:
420 = 1080
Since the equation is not true, it means there is no consistent solution for 'u' and 'a'. There must be an error in the given data or the problem itself.
Please double-check the values provided for displacement and time, or provide any additional information that might help in resolving this discrepancy.