A body covers 30m and 40m during 10th and 15th second respectively. The acceleration and initial velocity of the body are?
To find the acceleration and initial velocity of the body, we can use the kinematic equation of motion:
s = ut + 0.5at²
Where:
s = Distance traveled
u = Initial velocity
t = Time
a = Acceleration
First, let's find the time taken to cover the distances of 30m and 40m during the 10th and 15th second, respectively.
For the 10th second:
s = 30m
t = 10s
30 = u(10) + 0.5a(10)²
30 = 10u + 50a --- (Equation 1)
For the 15th second:
s = 40m
t = 15s
40 = u(15) + 0.5a(15)²
40 = 15u + 112.5a --- (Equation 2)
We now have two equations with two unknowns (u and a). We can solve these equations simultaneously to find the values of u and a.
From Equation 1:
u = (30 - 50a)/10 --- (Equation 3)
Substitute the value of u from Equation 3 into Equation 2:
40 = 15((30 - 50a)/10) + 112.5a
Simplify and solve for a:
40 = (450 - 750a)/10 + 112.5a
40 = 45 - 75a + 112.5a
40 - 45 = 112.5a - 75a
-5 = 37.5a
a = -5/37.5
a = -0.133 m/s²
Now substitute the value of a into Equation 3 to find u:
u = (30 - 50(-0.133))/10
u = 3.3 m/s
Therefore, the acceleration of the body is -0.133 m/s² (negative sign indicating deceleration) and the initial velocity of the body is 3.3 m/s.