a body at rest is given an initial uniform acceleration of 18m/s squre for 30sec after which the acceleration is reduced to 5m/s squre for the next 20sec. the body maintains the speed attained for 60sec after which it is brought to rest in 20sec. a)draw the velocity time graph of the motion bi)using the graph calculate the maximum speed attained during the motion. ii)calculate the average retardation as the body is being brought to rest. iii)calculate the total distance traveled during the first 50sec iv)calculate the average speed during the same intervals as seen in question iii?

All_for_one

2 years ago

I'm here to help with your physics problem. Let's start by addressing each part of the question.

a) Velocity-time graph:
To draw the velocity-time graph, we'll consider the different stages of the motion:
1. Initial acceleration of 18 m/s^2 for 30 seconds
2. Reduced acceleration of 5 m/s^2 for the next 20 seconds
3. Maintaining the speed attained for 60 seconds
4. Bringing the body to rest in 20 seconds

For the first stage:
The initial velocity, u = 0 (as the body is at rest)
Acceleration, a = 18 m/s^2
Time, t = 30 seconds
Using the equation v = u + at, we can find the final velocity at the end of this stage.

For the second stage:
The initial velocity is the final velocity from the previous stage.
Acceleration, a = 5 m/s^2
Time, t = 20 seconds
Using the equation v = u + at, we can find the final velocity at the end of this stage.

For the third stage:
The body maintains the speed attained for 60 seconds, so the velocity is constant.

For the fourth stage:
We need to bring the body to rest, so there will be a deceleration.

b) Maximum speed attained:
To calculate the maximum speed attained, we'll find the highest point on the velocity-time graph.

ii) Average retardation:
To calculate the average retardation as the body is being brought to rest, we'll use the formula for average acceleration/deceleration.

iii) Total distance traveled during the first 50 seconds:
We can use the area under the velocity-time graph to find the total distance traveled during the first 50 seconds.

iv) Average speed during the same intervals as seen in question iii:
To find the average speed, we'll divide the total distance traveled by the time taken.

Let's start by calculating the velocity at the end of each stage and then proceed to the other parts of the question.