An object moving with a constant accleration travels distance of 20m and 24m respectively in 3rd and 4th second of its motion. Find the initial velocity and the accleration of an object
To find the initial velocity and acceleration of the object, we can use the equations of motion that relate distance, initial velocity, acceleration, and time.
Let's denote the initial velocity of the object as "u" and the acceleration as "a."
We are given the following information:
- In the 3rd second, the distance traveled is 20m.
- In the 4th second, the distance traveled is 24m.
Using the equation of motion for distance (s) in terms of initial velocity (u), acceleration (a), and time (t):
s = ut + (1/2)at^2
For the 3rd second: s = 20m, t = 3s
20m = u(3s) + (1/2)a(3s)^2
20m = 3u + 9/2a (equation 1)
For the 4th second: s = 24m, t = 4s
24m = u(4s) + (1/2)a(4s)^2
24m = 4u + 8a (equation 2)
We now have a system of two equations with two unknowns (u and a).
To solve this system of equations, we can use the method of substitution or elimination.
Using the elimination method, we will eliminate the variable "u."
Multiply equation 1 by 4:
80m = 12u + 18a (equation 1 multiplied by 4)
24m = 4u + 8a (equation 2)
Subtract equation 2 from equation 1 multiplied by 4:
80m - 24m = 12u + 18a - 4u - 8a
56m = 8u + 10a
Simplify:
7m = u + 5/4a (equation 3)
Now, substitute equation 3 into equation 2 to solve for "a":
24m = 4(u + 5/4a) + 8a
24m = 4u + 5a + 8a
24m = 4u + 13a
Now, we have a new equation:
24m = 4u + 13a (equation 4)
We can solve equations 3 and 4 as a system of linear equations to find the values of "u" and "a."
Subtract equation 4 from equation 3 multiplied by 4:
28m - 24m = 4u + 5/4a - 4u - 13a
4m = -12a - 9/4a
4m = -48/4a - 9/4a
4m = -57/4a
Multiply both sides by 4/57:
16m/57 = a
Now substitute the value of "a" back into equation 3 to solve for "u":
7m = u + 5/4a
7m = u + 5/4(-16m/57)
7m = u - 20m/57
Multiply both sides by 57 to eliminate the fraction:
399m = 57u - 20m
Combining like terms:
419m = 57u
Divide both sides by 57:
u = 419m/57
Therefore, the initial velocity of the object is u = 419m/57, and the acceleration is a = 16m/57.