A car starts from rest and accelerate uniformely at 4m/s^2 for 6 seconds. for the next 8 sec. the driver moves with constant velocity. After this the driver applies brakes and stops the car in 10 sec. What is the total distance travelled by the car?
V1 = a*t = 4 * 6 = 24 m/s.
d1 = 0.5a*t^2 = 0.5*4*6^2 = 72 m.
d2 = V*t = 24 * 8 = 192 m.
V = Vo + a*t = 0.
a = -Vo/t = -24/10 = -2.4 m/s^2.
V^2 = Vo^2 + 2a*d = 0.
d3 = -(Vo^2)/2a = -(24^2)/-4.8 = 120 m.
d = d1+d2+d3.
To find the total distance traveled by the car, we need to calculate the distance traveled during each phase of its motion: the acceleration phase, the constant velocity phase, and the braking phase.
1. Acceleration phase:
During this phase, the car starts from rest and accelerates uniformly at 4 m/s^2 for 6 seconds. To calculate the distance traveled during acceleration, we can use the kinematic equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the car starts from rest, the initial velocity is 0. Plugging in the values, we get:
distance = (0 * 6) + (0.5 * 4 * 6^2)
distance = 0 + (0.5 * 4 * 36)
distance = 0 + (0.5 * 144)
distance = 0 + 72
distance = 72 meters
2. Constant velocity phase:
During this phase, the driver moves with constant velocity for 8 seconds. Since velocity is constant, we can find the distance by multiplying the velocity by time:
distance = velocity * time
The velocity during this phase is the final velocity reached at the end of the acceleration phase. We can calculate it using another kinematic equation:
final velocity = initial velocity + (acceleration * time)
Since the initial velocity is 0 and the acceleration is 4 m/s^2, the final velocity is:
final velocity = 0 + (4 * 6)
final velocity = 0 + 24
final velocity = 24 m/s
Plugging in the values, we get:
distance = 24 * 8
distance = 192 meters
3. Braking phase:
During this phase, the car applies brakes and stops in 10 seconds. The distance traveled during deceleration can be calculated using the same kinematic equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the final velocity is 0 (the car stops), the initial velocity is the final velocity reached at the end of the constant velocity phase, which is 24 m/s. The acceleration is negative because it opposes the motion and slows down the car. Taking these values into account, we get:
distance = (24 * 10) + (0.5 * -4 * 10^2)
distance = 240 + (-2 * 100)
distance = 240 - 200
distance = 40 meters
Total Distance Traveled = distance during acceleration + distance during constant velocity + distance during deceleration
Total Distance Traveled = 72 + 192 + 40
Total Distance Traveled = 304 meters
Therefore, the car traveled a total distance of 304 meters.