A tram starts from rest atone station and comes to a stop one minute later at the next. It accelerates uniformly at 2m/s2 until it reaches a speed of 20m/s. It travels at this constant speed for a certain time until it decelerates back to rest at 4m/s2. Find the average velocity of the tram over the entire journey.

The average velocity=distance/time, time=60s

distance=2*10^2/2+20*45+4*5^2/2=1050m

To find the average velocity of the tram over the entire journey, we need to calculate the total displacement and total time taken.

Let's break down the journey into three parts: the acceleration phase, the constant speed phase, and the deceleration phase.

1. Acceleration Phase:
During this phase, the tram starts from rest and accelerates uniformly until it reaches a speed of 20 m/s. We need to find the time it takes for the tram to reach 20 m/s.

Using the formula for uniform acceleration:
v = u + at
where:
v = final velocity (20 m/s)
u = initial velocity (0 m/s)
a = acceleration (2 m/s^2)
t = time taken

Substituting the values, we get:
20 = 0 + 2t
Solving for t, we find:
t = 20/2
t = 10 seconds

During this phase, the distance covered can be found using:
s = ut + (1/2)at^2
where:
s = displacement
u = initial velocity (0 m/s)
a = acceleration (2 m/s^2)
t = time taken (10 seconds)

Substituting the values, we get:
s = 0 * 10 + (1/2) * 2 * (10^2)
s = 0 + 100
s = 100 meters

2. Constant Speed Phase:
During this phase, the tram travels at a constant speed of 20 m/s. The displacement in this phase can be found using:
s = vt
where:
s = displacement
v = velocity (20 m/s)
t = time

Since the time duration for this phase is not given, we will use the fact that the total journey takes 1 minute (60 seconds), and the acceleration and deceleration phases each take 10 seconds.

Therefore, the time for the constant speed phase is:
Total time - (Acceleration time + Deceleration time)
60 seconds - (10 seconds + 10 seconds) = 40 seconds

Using the formula, we get:
s = 20 * 40
s = 800 meters

3. Deceleration Phase:
During this phase, the trams decelerates at 4 m/s^2 until it comes to a stop. Since the tram starts from a speed of 20 m/s, we need to find the time it takes to decelerate to 0 m/s.

Using the same formula as in the first phase:
v = u + at
where:
v = final velocity (0 m/s)
u = initial velocity (20 m/s)
a = acceleration (-4 m/s^2) [negative because it's deceleration]
t = time taken

Substituting the values, we get:
0 = 20 - 4t
4t = 20
t = 20 / 4
t = 5 seconds

Using the formula for displacement:
s = ut + (1/2)at^2
where:
s = displacement
u = initial velocity (20 m/s)
a = acceleration (-4 m/s^2)
t = time taken (5 seconds)

Substituting the values, we get:
s = 20 * 5 + (1/2) * (-4) * (5^2)
s = 100 - 50
s = 50 meters

Now, to find the average velocity over the entire journey, we need to calculate the total displacement and total time taken:

Total displacement = Displacement in acceleration phase + Displacement in constant speed phase + Displacement in deceleration phase
Total displacement = 100 + 800 + 50
Total displacement = 950 meters

Total time taken = Time in acceleration phase + Time in constant speed phase + Time in deceleration phase
Total time taken = 10 + 40 + 5
Total time taken = 55 seconds

Finally, Average velocity = Total displacement / Total time taken
Average velocity = 950 / 55
Average velocity ≈ 17.27 m/s

Therefore, the average velocity of the tram over the entire journey is approximately 17.27 m/s.