Problem:
A moving tray is brought to rest within 20 seconds by applying brakes. Find its initial velocity of the deceleration due to brakes in m/s².

Solution:

Given:
Time taken to bring the tray to rest (t) = 20 s

Formula:
The formula to calculate velocity is:

v = u + at

Where:
v = final velocity (0 m/s, as the tray is brought to rest)
u = initial velocity
a = acceleration
t = time taken

Acceleration:
The acceleration can be calculated using the formula:

a = (v - u) / t

Since the final velocity is 0 m/s, the formula becomes:

a = (-u) / t

Substituting Values:
We are given that the time taken to bring the tray to rest (t) is 20 seconds. Substituting this value into the formula:

a = (-u) / 20

Acceleration due to Brakes:
The acceleration due to brakes is given as -2 m/s². Since the tray is decelerating, the acceleration is negative.

Equating Accelerations:
We can equate the two accelerations to find the initial velocity:

-2 = (-u) / 20

Calculating Initial Velocity:
To find the initial velocity (u), we can solve the equation:

-2 * 20 = -u

-40 = -u

u = 40 m/s

Explanation:
- The tray is brought to rest within 20 seconds by applying brakes.
- We can use the formula v = u + at to find the initial velocity.
- The acceleration can be calculated using the formula a = (v - u) / t.
- Since the final velocity is 0 m/s, the equation simplifies to a = (-u) / t.
- We are given that the time taken (t) is 20 seconds.
- Substituting this value into the formula, we get a = (-u) / 20.
- The acceleration due to brakes is given as -2 m/s².
- Equating the two accelerations, we get -2 = (-u) / 20.
- Solving this equation, we find the initial velocity (u) to be 40 m/s.
- Therefore, the initial velocity of the tray before applying brakes was 40 m/s.