a car starting from rest is accelerated at 2m/s(square) for 10s, then moves at constant velocity for 20s and then decelerates at 1m/s(square), finally stops. how far does it travel during its trip? please help me! I need in solution for that problem

a = 2

v = 2t + c, where t is in seconds
when t=0, v = 0 , (it started from rest)
0 = 0 + c, c = 0

v = 2t

s = t^2 + k
when t = 0, s = 0 , (hasn't gone anywhere)

after 10 seconds
v = 20 m/s
s = 100 m

now goes for 20 s, at 20 m/s, covering 400 m
so it can covered 500 m, and the speed is 20 m/s

now repeat the process: starting again with a time of t=0, v = 20, s=0 (remembering we have already gone 500 m)
a = -1
v = -t + p
when t = 0, v = 20
20 = 0 + p
so v = -t + 20
s = (-1/2)t^2 + 20t + q
q = 0
s = (-1/2)t^2 + 20t

when it came to a stop, v = 0
0 = -t + 20
t = 20, so it took 20 seconds to stop
in those 20 seconds, the car went another
(-1/2)(20)^2 + 20(20) m
= 200 m

so the whole "trip" was 700 m

To find the total distance traveled by the car during its trip, we need to calculate the distance traveled during each phase of its motion.

Phase 1: Acceleration
Acceleration (a) = 2 m/s²
Time (t) = 10 seconds

To find the distance traveled during acceleration, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time²)

The car starts from rest, so the initial velocity is 0.
distance = (0 * 10) + (0.5 * 2 * 10²)
distance = 0 + 0.5 * 2 * 100
distance = 100 meters

Phase 2: Constant Velocity
The car moves at a constant velocity for 20 seconds. The distance traveled during constant velocity is velocity multiplied by time.

Velocity = final velocity = the velocity attained at the end of acceleration
So,
Velocity = accelerator = (initial velocity) + (acceleration * time)
= 0 + (2 * 10)
= 20 m/s

distance = velocity * time = 20 * 20 = 400 meters

Phase 3: Deceleration
Deceleration (a) = 1 m/s²
Time (t) = unknown

The car decelerates until it stops. We need to find the time taken to decelerate from the constant velocity to a stop.

Final velocity (v) = 0 (since the car comes to a stop)
Using the equation:
final velocity = initial velocity + (acceleration * time)
0 = 20 + (-1 * t)
-20 = -t
t = 20 seconds

Using the equation for distance:
distance = (initial velocity * time) + (0.5 * acceleration * time²)
distance = (20 * 20) + (0.5 * 1 * 20²)
distance = 400 + (0.5 * 1 * 400)
distance = 400 + 200
distance = 600 meters

Finally, the total distance traveled during the entire trip is the sum of the distances traveled in each phase:
Total distance = distance during acceleration + distance during constant velocity + distance during deceleration
Total distance = 100 + 400 + 600
Total distance = 1100 meters

Therefore, the car travels a total distance of 1100 meters during its trip.