A body covers 30m & 40m during 10th & 15 th second respectively the acceleration and initial body are respectively
the average speed from t = 9 to t = 10 is 30 m/s call it Va
the average speed from t = 14 to t = 15 is 40 m/s Call it Vb
so
x....... v....... t
Xi .....Vi ... ..0
Xa ....30.... 9.5
Xb ....40 ....14.5
If a is constant
v = Vi + at
x = Xi + Vi t + (1/2) a t^2
Xb = Xi + Vi (14.5) + (1/2) a (14.5)^2
Xa = Xi + Vi(9.5) + (1/2) a (9.5)^2
Vb = Vi + a(14.5)
Va = Vi + a(9.5)
---------------------------subtract,
Vb - Va = 40-30 = 10 = a (14.5-9.5) = a (5)
so
a = 2 m/s^2
now work on Vi
Xb - Xa = average speed from t = 9.5 to 14.5 times 5 seconds
= 35 * 5 = 175 m
so
175 = 5 Vi + (1/2)2(14.5^2-9.5^2)
175 = 5 Vi + (210-90)
175 = 5 Vi + 120
Vi = 11 m/s
To find the acceleration and initial velocity of the body, we can use the equations of motion.
First, let's write down the given information:
- The body covers a distance of 30m during the 10th second.
- The body covers a distance of 40m during the 15th second.
Now, we need to use the equation of motion to find the acceleration (a) and initial velocity (u).
The equation of motion we can use is:
s = ut + (1/2)at^2
Where:
s is the distance covered,
u is the initial velocity,
t is the time, and
a is the acceleration.
Let's solve this step by step:
Step 1: Finding the acceleration (a)
We know that the body covers a distance of 30m during the 10th second. So, we can plug in the values as follows:
30 = u * 10 + (1/2) * a * (10^2) --- Equation (1)
Next, we know that the body covers a distance of 40m during the 15th second. Plugging in the values:
40 = u * 15 + (1/2) * a * (15^2) --- Equation (2)
Step 2: Solving for initial velocity (u)
To find the initial velocity (u), we can rearrange Equation (1) to solve for u:
u = (30 - (1/2) * a * (10^2)) / 10 --- Equation (3)
Step 3: Substitute the value of u from Equation (3) into Equation (2)
Plugging in the value of u from Equation (3) into Equation (2) gives us:
40 = ((30 - (1/2) * a * (10^2)) / 10) * 15 + (1/2) * a * (15^2)
Now, we can solve this equation to find the value of acceleration (a).
Following these steps will lead us to the solution for the acceleration and initial velocity of the body.