1 a cyclist moving on a circular track of radius 100m completes one revolution in 2 minutes what is his average speed and average velocity in one full revolution.
2 moving with uniform acceleration a body covers150m during 10 sec so that it covers 24m during the 10th sec wat is the initial velocity and acceleration of the bdy
To solve these problems, we will use the formulas for average speed, average velocity, initial velocity, and acceleration.
1. Average speed is defined as the total distance traveled divided by the total time taken. In this case, the cyclist completes one full revolution, which means the distance traveled is equal to the circumference of the circular track. The formula for the circumference of a circle is C = 2 * π * r, where r is the radius. In this case, the radius is given as 100m. So, the circumference of the circular track is C = 2 * π * 100m = 200πm. The time taken to complete one full revolution is given as 2 minutes, which is equivalent to 2 * 60 = 120 seconds.
Average speed = Total distance traveled / Total time taken
Average speed = 200πm / 120s
Average speed ≈ 5.24 m/s
2. To find the initial velocity and acceleration of the body, we can use the equations of motion. We are given the total distance covered (150m) and the time taken (10 seconds). We are also given that the body covers 24m during the 10th second.
Let's call the initial velocity "u" and the acceleration "a."
Using the equation of motion:
Distance covered = initial velocity * time + (1/2) * acceleration * time^2
For the first 9 seconds, the distance covered is 150m. So:
Distance covered = u * 9s + (1/2) * a * (9s)^2
150m = 9u + 81a (Equation 1)
Now, let's consider the 10th second. We are given that the body covers 24m during this time:
Distance covered = u * 10s + (1/2) * a * (10s)^2
24m = 10u + 100a (Equation 2)
We now have a system of two equations (Equation 1 and Equation 2) with two unknowns (u and a). We can solve this system of equations to find the values of u and a using substitution or elimination.
From Equation 1, we can rearrange it to solve for u:
u = (150m - 81a) / 9s (Equation 3)
Now, substitute the value of u from Equation 3 into Equation 2:
24m = 10[(150m - 81a) / 9s] + 100a
Simplifying:
24m = (1650m - 900a) / 9s + 100a
Multiply both sides by 9s to eliminate the fraction:
24m * 9s = 1650m - 900a + 900s * 100a
216ms = 1650m + (900s * 100 - 900)a
216ms = 1650m + 90000sa - 900a
216ms = 1650m + (90000s - 900)a
216ms = 1650m + 900(100s - 1)a
Comparing the coefficients on both sides, we have:
216 = 1650
900(100s - 1) = 900
Since the coefficients are equal, we can conclude that both terms are independent and equal to zero:
1650m = 216; solving for m, we get m ≈ 0.131 m/s
100s - 1 = 0; solving for s, we get s = 0.01
Substituting the values of m and s back into Equation 3, we can find the initial velocity (u):
u = (150m - 81a) / 9s
u = (150 * 0.131 - 81a) / (9 * 0.01)
u ≈ 19.273 - 9a
So, the initial velocity (u) is approximately 19.273 - 9a, and the acceleration (a) is approximately 0.131 m/s².
average speed = total distance /total time
radius=50m so circumference=2*22/7*50
= 311.43/4
=7.85
1. Average speed = total distance travelled/ total time taken = 2•π•100/2•60 = 5.24 m/s,
Displacement is the distance from starting point to the end point.
Average velocity = final displacement/total time taken = 0/t =0.
2.
s =vₒ•t +a•t²/2,
v(9) = vₒ +a•9,
24 =v(9) •1 + a•1²/2 =
=vₒ +a•9 + a•1²/2 =
= vₒ +9.5•a.
s =vₒ•t +a•t²/2 =>
150 = vₒ•10+ a•100/2 =
= 10• vₒ + 50•a.
24= vₒ +9.5•a,
150= 10• vₒ + 50•a.
45° = 90,
a = 2 m/s².
vₒ = 24-9.5 •a = 5 m/s.