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

ave) = total distance/ total time =s/t

t=s/v(ave) = 100/20 = 5 s

s=v₀t+at²/2 ….(1)
v= v₀+at
a= (v -v₀)/t ….(2)
Substitute (2) in (1)
2s= v₀t +vt
v₀ =( 2s –vt)/t =( 200 -25•5)/5 = 15 m/s
a=(v -v₀)/t =(25-15)/5 = 2 m/s²

To find the initial velocity and acceleration of the car, we can use the equations of motion. We are given the following information:

Distance (s) = 100m
Average velocity (v_avg) = 20m/s
Final velocity (v_f) = 25m/s

First, we can use the formula for average velocity:

v_avg = (v_i + v_f) / 2

Rearranging the formula, we can solve for the initial velocity (v_i):

v_i = 2 * v_avg - v_f

Substituting the given values, we have:

v_i = 2 * 20m/s - 25m/s
v_i = 40m/s - 25m/s
v_i = 15m/s

The initial velocity of the car is 15m/s.

Now, we can use the equation of motion to find the acceleration (a):

v_f^2 = v_i^2 + 2 * a * s

Rearranging the formula, we can solve for acceleration (a):

a = (v_f^2 - v_i^2) / (2 * s)

Substituting the given values, we have:

a = (25m/s)^2 - (15m/s)^2 / (2 * 100m)
a = 625m^2/s^2 - 225m^2/s^2 / 200m
a = 400m^2/s^2 / 200m
a = 2m/s^2

The acceleration of the car is 2m/s^2.

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