A car start from rest accelerating at 6.0mls for 5secs. It continues at this speed for 25secs and then comes to a stop in 4s calculate (a). The total displacement (b). The average velocity for the whole displacement
You mean 6 m/s^2 I thinlk
v = 0 + a t = 6 * 5 = 30 m/s at 5 sec
d = Xi + Vi t + (1/2) a t^2 = 0 + 0 + (6/2)(25) = 75 meters from start
goes further 25 s at 30 m/s
d = 25 *30 = 750 meters more
x = 75 + 750 = 825 meters from start
stops from 30 m/s in 4 s
0 = 30 + a*4
so a = - 30/4 = - 7.5
d = 15*4 = 60 meters more
total x = 75 + 60 = 135 meters from start
how long did it take?
5 + 25 +4 = 34 seconds
sorry, 825 + 60 = 885
To solve this problem, we can break it down into three parts:
Part (a): Calculating total displacement.
To find the total displacement, we need to calculate the displacement for each part of the motion, namely the acceleration phase, the constant velocity phase, and the deceleration phase.
1. Acceleration phase:
The car starts from rest and accelerates at 6.0 m/s^2 for 5 seconds.
We can use the formula:
displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
Given:
initial velocity (u) = 0 m/s (as the car starts from rest)
acceleration (a) = 6.0 m/s^2
time (t) = 5 s
Plugging the values into the formula:
displacement = (0 * 5) + (0.5 * 6.0 * 5^2)
displacement = 0 + (0.5 * 6.0 * 25)
displacement = 0 + 75
displacement = 75 meters
2. Constant velocity phase:
The car continues at a constant velocity for 25 seconds.
Since the velocity remains constant, the displacement during this phase is simply the product of the velocity and time.
velocity (v) = 6.0 m/s
time (t) = 25 s
displacement = velocity * time
displacement = 6.0 * 25
displacement = 150 meters
3. Deceleration phase:
The car comes to a stop in 4 seconds.
In this case, the car is decelerating, so the displacement formula will be the same as during the acceleration phase.
initial velocity (u) = 6.0 m/s (as the velocity is constant at this point)
acceleration (a) = -6.0 m/s^2 (negative because deceleration)
time (t) = 4 s
displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
displacement = (6.0 * 4) + (0.5 * -6.0 * 4^2)
displacement = 24 + (-6.0 * 8)
displacement = 24 - 48
displacement = -24 meters
Now, we can find the total displacement by summing up the displacements from each phase:
Total displacement = acceleration phase + constant velocity phase + deceleration phase
Total displacement = 75 + 150 + (-24)
Total displacement = 201 meters
Therefore, the total displacement is 201 meters.
Part (b): Calculating average velocity for the whole displacement.
The average velocity can be calculated by dividing the total displacement by the total time taken.
Total time taken = time during acceleration phase + time during constant velocity phase + time during deceleration phase
Total time taken = 5 + 25 + 4
Total time taken = 34 seconds
Average velocity = total displacement / total time taken
Average velocity = 201 / 34
Average velocity ≈ 5.91 m/s
Therefore, the average velocity for the whole displacement is approximately 5.91 m/s.