To determine the final velocity and the time taken by the car to travel a distance of 100 m with a constant acceleration of 3 m/s², we can use the equations of motion.
The equation that relates distance (d), initial velocity (u), final velocity (v), acceleration (a), and time (t) is:
d = ut + (1/2)at^2
Given that the car starts from rest (u = 0), the equation simplifies to:
d = (1/2)at^2
Plugging in the known values:
100 = (1/2)(3)t^2
Simplifying the equation:
200 = 3t^2
Dividing both sides by 3:
t^2 = 200/3
Taking the square root of both sides:
t ≈ √(200/3)
t ≈ 8.16 seconds (rounded to two decimal places)
So, the time taken to travel 100 m is approximately 8.16 seconds.
To find the final velocity (v), we can use the equation:
v = u + at
Since the initial velocity (u) is 0, the equation simplifies to:
v = at
Plugging in the values:
v = (3)(8.16)
v ≈ 24.49 m/s (rounded to two decimal places)
Therefore, the final velocity of the car is approximately 24.49 m/s.