A record of travel along a straight path is as follows:

(a) Start from rest with constant acceleration of 3.51 m/s2 for 17.8 s;
(b) Constant velocity of 62.478 m/s for the next 0.946 min;
(c) Constant negative acceleration of
−10.9 m/s2 for 3.89 s.
What was the total displacement x for the
complete trip?

To find the total displacement for the complete trip, we need to calculate the displacements for each segment of the trip and then sum them up.

(a) Start from rest with constant acceleration of 3.51 m/s^2 for 17.8 s:

Using the equation: d = v_i*t + 0.5*a*t^2

Initial velocity (v_i) = 0 (since starting from rest)
Time (t) = 17.8 s
Acceleration (a) = 3.51 m/s^2

Plugging in the values, we can calculate the displacement for this segment:

d1 = 0*t + 0.5*a*t^2
d1 = 0 + 0.5*3.51*17.8^2
d1 = 0 + 0.5*3.51*316.84
d1 = 0 + 555.8166
d1 ≈ 555.82 m

(b) Constant velocity of 62.478 m/s for the next 0.946 min (convert to seconds):

Time (t) = 0.946 min * 60 s/min
t = 56.76 s

Since the velocity is constant, the displacement for this segment is simply:

d2 = v*t
d2 = 62.478 * 56.76
d2 ≈ 3553.54 m

(c) Constant negative acceleration of -10.9 m/s^2 for 3.89 s:

Time (t) = 3.89 s
Acceleration (a) = -10.9 m/s^2

Plugging in the values, we can calculate the displacement for this segment:

d3 = v_i*t + 0.5*a*t^2
d3 = 62.478 * 3.89 + 0.5 * -10.9 * 3.89^2
d3 ≈ 241.9999 m

To find the total displacement, we sum up the displacements:

Total displacement (x) = d1 + d2 + d3
x = 555.82 + 3553.54 + 241.9999
x ≈ 4351.36 m

Therefore, the total displacement for the complete trip is approximately 4351.36 m.

To find the total displacement for the complete trip, we need to calculate the displacement for each segment of the travel and then add them up.

Segment (a):
We can calculate the displacement using the formula:
d = v_0*t + (1/2)*a*t^2
where d is the displacement, v_0 is the initial velocity, a is the acceleration, and t is the time.

Given:
Initial velocity (v_0) = 0 m/s (start from rest)
Acceleration (a) = 3.51 m/s^2
Time (t) = 17.8 s

Using the formula:
d_a = (0)*(17.8) + (1/2)*(3.51)*(17.8)^2

Segment (b):
Since the velocity is constant, the displacement is given by:
d_b = v * t
where v is the velocity and t is the time.

Given:
Velocity (v) = 62.478 m/s
Time (t) = 0.946 min = 0.946 * 60 = 56.76 s

Using the formula:
d_b = (62.478)*(56.76)

Segment (c):
Again, we can use the same formula to calculate the displacement:
d_c = v * t
where v is the velocity and t is the time.

Given:
Velocity (v) = 62.478 m/s (constant negative acceleration signifies that the object is slowing down, but the velocity remains the same)
Time (t) = 3.89 s

Using the formula:
d_c = (62.478)*(3.89)

Now, we can calculate the total displacement by adding up the displacements of each segment:
Total displacement (x) = d_a + d_b + d_c

Just substitute the calculated values into the equation and solve to get the answer for the total displacement.