To determine the acceleration (a) and displacement (s) of a car starting from rest and attaining a velocity of 20 m/s in a time of 3 seconds, we can use the equations of motion. The relevant equation in this case is:
v = u + at
Where: v = final velocity u = initial velocity a = acceleration t = time
Since the car starts from rest, the initial velocity (u) is 0 m/s. The final velocity (v) is 20 m/s, and the time (t) is 3 seconds. We can rearrange the equation to solve for the acceleration (a):
a = (v - u) / t a = (20 m/s - 0 m/s) / 3 s a = 20 m/s / 3 s a ≈ 6.67 m/s²
So the acceleration of the car is approximately 6.67 m/s².
To calculate the displacement (s), we can use another equation of motion:
s = ut + (1/2)at²
Since the initial velocity (u) is 0 m/s, the equation simplifies to:
s = (1/2)at² s = (1/2)(6.67 m/s²)(3 s)² s = (1/2)(6.67 m/s²)(9 s²) s = (3.33 m/s²)(9 s²) s ≈ 30 m
So the displacement of the car from its starting position is approximately 30 meters.