A record of travel along a straight path is as follows:
1. Start from rest with constant acceleration of 2.59 m/s2 for 19.0 s.
2. Maintain a constant velocity for the next 2.15 min.
3. Apply a constant negative acceleration of −9.08 m/s2 for 5.42 s.
(a) What was the total displacement for the trip?
1. Vo = a*t = 2.59 * 19 = 49.21 m/s.
d1 = 0.5a*t^2 = 0.5*2.59*19^2 = 467.5 m.
2. d2 = Vo*t = 49.21 * (2.15*60)=6348 m.
3. V = a*t = -9.08 * 5.42 = -49.21 m/s.
V-Vo = 49.21-49.21 = 0 = Final velocity.
d3 = (Vf^2-Vo^2)/2g. Vf = 0
d3 = -(Vo^2)/2g = -(49.21^2)/-19.6 = 124 m.
a. D = d1+d2+d3 = 468 + 6348 + 124 =
6940 m.
To find the total displacement for the trip, we need to calculate the displacement during each phase of the motion and then add them together.
Phase 1: Start from rest with constant acceleration of 2.59 m/s^2 for 19.0 s.
In this phase, we need to find the displacement using the equation:
s = ut + (1/2)at^2,
where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Given:
u = 0 m/s (initial velocity at rest)
a = 2.59 m/s^2 (acceleration)
t = 19.0 s
Plugging in the values, we get:
s1 = (0)(19) + (1/2)(2.59)(19)^2
s1 = 0 + (1/2)(2.59)(361)
s1 = 0 + 468.99
s1 = 468.99 m
Phase 2: Maintain a constant velocity for the next 2.15 min.
Since the velocity is constant during this phase, the displacement can be calculated using the equation:
s = v * t,
where s is the displacement, v is the constant velocity, and t is the time.
Given:
v = constant velocity
t = 2.15 min = 2.15 * 60 = 129 s (converting minutes to seconds)
Plugging in the values, we get:
s2 = v * t
Phase 3: Apply a constant negative acceleration of -9.08 m/s^2 for 5.42 s.
Similar to phase 1, we can calculate the displacement using the equation:
s = ut + (1/2)at^2,
where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Given:
u = velocity at the end of phase 2
a = -9.08 m/s^2 (negative acceleration)
t = 5.42 s
Plugging in the values, we get:
s3 = (u)(5.42) + (1/2)(-9.08)(5.42)^2
s3 = (u)(5.42) + (1/2)(-9.08)(29.3764)
s3 = (u)(5.42) - 133.201792
s3 = -133.201792 + 5.42u
To find the value of u, we need more information.