A car is initially at rest on a straight road. The car accelerates uniformly for a distance of 200 meters over a time interval of 10 seconds. After reaching the end of this distance, the car continues to travel at a constant velocity for an additional 5 seconds. The car then decelerates uniformly to a complete stop in 3 seconds.
a) Determine the acceleration of the car during the first phase.
b) Calculate the final velocity of the car after the constant velocity phase.
c) Find the deceleration of the car during the third phase.
a) To determine the acceleration of the car during the first phase, we can use the kinematic equation:
v = u + at
Where: v = final velocity (unknown) u = initial velocity (0 m/s, since the car is initially at rest) a = acceleration (unknown) t = time (10 seconds)
Since the initial velocity is 0 m/s, the equation simplifies to:
v = at
Substituting the given values:
v = a * 10
We also know that the car traveled a distance of 200 meters during this time interval. Using the kinematic equation:
s = ut + (1/2) * a * t^2
Since the initial velocity is 0 m/s, the equation simplifies to:
s = (1/2) * a * t^2
Substituting the given values:
200 = (1/2) * a * 10^2
Simplifying the equation:
200 = 50a
a = 200/50
a = 4 m/s^2
Therefore, the acceleration of the car during the first phase is 4 m/s^2.
b) During the constant velocity phase, the car travels with a constant velocity. Therefore, the final velocity of the car after this phase will be the same as its velocity during this phase. Thus, the final velocity after the constant velocity phase is:
Final velocity = 4 m/s (since the velocity is constant and equal to the acceleration during the first phase)
c) In the third phase, the car decelerates uniformly and comes to a complete stop. We can use the same kinematic equation as in part a:
v = u + at
Since the final velocity is 0 m/s (coming to a complete stop), the equation becomes:
0 = 4 + (-a) * 3
Simplifying the equation:
-3a = -4
a = 4/3 m/s^2
Therefore, the deceleration of the car during the third phase is 4/3 m/s^2.
In summary:
a) The acceleration of the car during the first phase is 4 m/s^2. b) The final velocity of the car after the constant velocity phase is 4 m/s. c) The deceleration of the car during the third phase is 4/3 m/s^2.