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.