Plot a velocity time graph of a motorcycle that accelerates from rest for 10 secs upto a velocity of 20 m/s . It maintains this velocity for a further 20 secs and then s so that it stops in 20 secs

first ten seconds...straight line sloping upwards.

horizontal line next 20 seconds, then last 20 seconds slopes down to zero velocity.

Sure! Let's break down the steps to plot the velocity-time graph for the motorcycle:

Step 1: Identify the significant time intervals:
- Acceleration phase: 0 to 10 seconds
- Constant velocity phase: 10 to 30 seconds
- Retardation phase: 30 to 50 seconds

Step 2: Determine the slope of each interval:
- Acceleration phase: The slope is positive because the motorcycle is gaining velocity.
- Constant velocity phase: The slope is zero since the velocity remains constant.
- Retardation phase: The slope is negative because the motorcycle is slowing down.

Step 3: Determine the values for each interval:
- Acceleration phase: The motorcycle starts at rest and reaches a velocity of 20 m/s within 10 seconds.
- Constant velocity phase: The motorcycle remains at a constant velocity of 20 m/s for 20 seconds.
- Retardation phase: The motorcycle slows down from 20 m/s to rest over a period of 20 seconds.

Step 4: Plot the graph:
On the y-axis, we plot the velocity (m/s). On the x-axis, we plot the time (seconds).

Acceleration phase:
- At 0 seconds, the velocity is 0 m/s.
- At 10 seconds, the velocity is 20 m/s.
Connect these two points with a straight line.

Constant velocity phase:
- From 10 seconds to 30 seconds, plot a horizontal line at 20 m/s.

Retardation phase:
- At 30 seconds, the velocity is 20 m/s.
- At 50 seconds, the velocity is 0 m/s.
Connect these two points with a straight line, but with a negative slope.

The resulting velocity-time graph will show an upward sloping line during the acceleration phase, a horizontal line during the constant velocity phase, and a downward sloping line during the retardation phase.

Note: The specific scale of the graph may vary depending on the units used for time and velocity.

To plot the velocity-time graph of a motorcycle with the given conditions, we can break the motion into three stages: acceleration, constant velocity, and deceleration.

1. Acceleration stage:
The motorcycle is initially at rest and accelerates for 10 seconds up to a velocity of 20 m/s. During acceleration, the velocity increases uniformly with time. The equation for calculating velocity during uniform acceleration is:
v = u + at
where:
- v is the final velocity
- u is the initial velocity (which is 0 m/s as the motorcycle starts from rest)
- a is the acceleration
- t is the time

In this case, the initial velocity (u) is 0 m/s, the final velocity (v) is 20 m/s, and the time (t) is 10 seconds. We need to find the acceleration (a). Rearranging the equation, we get:
a = (v - u) / t
a = (20 - 0) / 10
a = 2 m/s²

Now we can calculate the velocity at different time intervals during the acceleration stage. Starting with t = 0, the initial time, the velocity will be 0 m/s. Then we can calculate the velocities at regular intervals, for example, every second, until t = 10 seconds.

2. Constant velocity stage:
After reaching the velocity of 20 m/s, the motorcycle maintains this constant velocity for 20 seconds. During this stage, the velocity remains constant, so the velocity-time graph will be a horizontal line at y = 20 m/s for the duration of 20 seconds.

3. Deceleration stage:
To bring the motorcycle to a stop in 20 seconds, it decelerates with uniform negative acceleration. The equation for calculating velocity during uniform deceleration is the same as the equation for acceleration, but with a negative sign:
v = u + at
Since the motorcycle is decelerating, the acceleration (a) will be negative. We know the initial velocity (u) is 20 m/s, the final velocity (v) is 0 m/s, and the time (t) is 20 seconds. Rearranging the equation, we get:
a = (v - u) / t
a = (0 - 20) / 20
a = -1 m/s²

Now we can calculate the velocities at regular intervals, starting from the final velocity of 20 m/s at t = 0, until t = 20 seconds.

Once you have all the calculated velocities at different time intervals for the three stages (acceleration, constant velocity, and deceleration), plot them on a graph with time on the x-axis and velocity on the y-axis.