A car travels a distance of 100m per second with a constant acceleration and average velocity of 20m per second .The final velocity acquired by the car is 25m per second .Find The initial velocity and acceleration of car

Vav=u+at

a=100m
Va=20m×1
v=25
U=100×25÷20
U=12.5m

To find the initial velocity and acceleration of the car, we can use the following equations of motion:

1. Final velocity squared = Initial velocity squared + 2 × acceleration × distance

2. Average velocity = (Initial velocity + Final velocity) / 2

Given:
- Final velocity (Vf) = 25 m/s
- Average velocity (Vavg) = 20 m/s
- Distance (d) = 100 m

Using equation (2), we can find the initial velocity:

Vavg = (Initial velocity + Final velocity) / 2

20 = (Initial velocity + 25) / 2

Multiply both sides of the equation by 2:

40 = Initial velocity + 25

Subtract 25 from both sides:

Initial velocity = 40 - 25 = 15 m/s

Now, we can use equation (1) to find the acceleration:

Final velocity squared = Initial velocity squared + 2 × acceleration × distance

25^2 = 15^2 + 2 × acceleration × 100

625 = 225 + 200 × acceleration

Subtract 225 from both sides:

400 = 200 × acceleration

Divide both sides by 200:

acceleration = 400 / 200 = 2 m/s^2

Therefore, the initial velocity of the car is 15 m/s and the acceleration is 2 m/s^2.

To find the initial velocity (u) and acceleration (a) of the car, we can use the following equations of motion:

1. Final velocity (v) = Initial velocity (u) + (Acceleration (a) * Time (t))
2. Average velocity (v_avg) = (Initial velocity (u) + Final velocity (v)) / 2
3. Distance (s) = (Initial velocity (u) * Time (t)) + (0.5 * Acceleration (a) * Time (t)^2)

From the given information:
- Final velocity (v) = 25 m/s
- Average velocity (v_avg) = 20 m/s
- Distance (s) = 100 m

To find the initial velocity (u):
Using equation 2, we can solve for u:
20 m/s = (u + 25 m/s) / 2

Simplifying the equation:
40 = u + 25
u = 40 - 25
u = 15 m/s

Therefore, the initial velocity of the car is 15 m/s.

To find the acceleration (a):
Using equations 1 and 3, we can solve for a:
25 m/s = 15 m/s + (a * t) ----(Equation 1)
100 m = (15 m/s * t) + (0.5 * a * t^2) ----(Equation 3)

Since we have two unknowns (a and t), we need another equation to solve for them. Unfortunately, the given information does not provide enough information to determine the acceleration and time.

Hence, the initial velocity of the car is 15 m/s, but the acceleration cannot be determined with the given information.