1. Start from rest with constant acceleration of 2.11 m/s2 for 20.0 s.
2. Maintain a constant velocity for the next 2.75 min.
3. Apply a constant negative acceleration of −8.44 m/s2 for 5.00 s.
(a) What was the total displacement for the trip?
Please explain with steps and an answer! Thank you!
draw the velocity (graph) vs time.
The area under the graph is distance, you can break the areas up into two triangles, and one rectangle, and count the squares (or use formulas for those ), add.
displacement=velocity*time
Step 1
v = 0 + 2.11 * 20 = 42.2 m/s
x = 0+0(20)+(1/2)*2.11*20^2=422 meters
so we are at 42.2 m/s and 422 m
Step 2
2.75*60 = 165 s
v = 42.2
x = 422 * 42.2 (165) + (1/2)*0*165^2
= 7385 meters
step 3
x = 7385 + 42.2(5) -(1/2)(8.44)(25)
= 7385 + 211 - 105.5
= 7491 meters
To find the total displacement for the trip, we need to calculate the displacement during each phase of motion and then sum them up.
Phase 1: Start from rest with constant acceleration of 2.11 m/s^2 for 20.0 s.
To find the displacement during this phase, we can use the kinematic equation:
s = ut + (1/2)at^2
where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.
Given:
u = 0 m/s (starting from rest),
a = 2.11 m/s^2,
t = 20.0 s,
Plugging in these values into the equation, we get:
s1 = (0)(20.0) + (1/2)(2.11)(20.0)^2
s1 = 0 + (1/2)(2.11)(400)
s1 = (1.055)(400)
s1 = 422.0 m
Phase 2: Maintain a constant velocity for 2.75 min.
Since the velocity is constant, there is no acceleration. Therefore, the displacement during this phase is given by:
s2 = v * t
where v is the constant velocity and t is the time.
Given:
t = 2.75 min = 2.75 * 60 s = 165.0 s
Plugging in the values, we get:
s2 = v * t
Phase 3: Apply a constant negative acceleration of -8.44 m/s^2 for 5.00 s.
Again, we can use the kinematic equation to find the displacement during this phase:
s = ut + (1/2)at^2
Given:
u = 0 m/s (starting from rest),
a = -8.44 m/s^2,
t = 5.00 s,
Plugging in the values, we get:
s3 = (0)(5.00) + (1/2)(-8.44)(5.00)^2
s3 = 0 + (1/2)(-8.44)(25.00)
s3 = (-4.22)(25.00)
s3 = -105.5 m
Now, let's add up the displacements from each phase to get the total displacement:
Total displacement = s1 + s2 + s3
Total displacement = 422.0 m + s2 - 105.5 m
Since we don't have the value for s2, we can't calculate the exact total displacement without it. Please provide the constant velocity during phase 2 (s2) to continue.