A cyclist is cycling at a uniform velocity of 8m/s for 8 seconds. He then stops paddling and

the cycle comes to rest in next ten seconds. Draw the velocity-time graph and calculate: (i)
the average retardation.(ii) the distance covered with uniform velocity.(iii) the distance
covered with variable velocity.(iv) the average velocity of the cyclist.

To draw the velocity-time graph, we will divide the motion into two parts: the uniform velocity phase and the deceleration phase.

(i) Uniform velocity phase:
During this phase, the cyclist is cycling at a uniform velocity of 8 m/s for 8 seconds. The velocity remains constant throughout this phase.

(ii) Deceleration phase:
After the uniform velocity phase, the cyclist stops paddling and the cycle comes to rest in the next 10 seconds. This means that the velocity decreases linearly from 8 m/s to 0 m/s in 10 seconds.

Now let's calculate the values:

(i) Average retardation:
The retardation is the rate at which the velocity decreases. Since the velocity decreases linearly, the average retardation can be calculated using the formula:

Retardation = Change in Velocity / Time taken

Change in Velocity = Final Velocity - Initial Velocity = 0 - 8 = -8 m/s
Time taken = 10 seconds

Retardation = -8 m/s / 10 s = -0.8 m/s^2

Therefore, the average retardation is -0.8 m/s^2.

(ii) Distance covered with uniform velocity:
The distance covered with uniform velocity can be calculated using the formula:

Distance = Velocity * Time

Velocity = 8 m/s
Time = 8 seconds

Distance = 8 m/s * 8 s = 64 meters

Therefore, the distance covered with uniform velocity is 64 meters.

(iii) Distance covered with variable velocity:
To calculate the distance covered in the deceleration phase (with variable velocity), we can use the equation:

Distance = (Initial Velocity + Final Velocity) / 2 * Time

Initial Velocity = 8 m/s
Final Velocity = 0 m/s
Time = 10 seconds

Distance = (8 m/s + 0 m/s) / 2 * 10 s = 40 meters

Therefore, the distance covered with variable velocity is 40 meters.

(iv) Average velocity:
Average velocity can be calculated using the formula:

Average Velocity = Total Distance / Total Time

Total Distance = Distance with uniform velocity + Distance with variable velocity
= 64 meters + 40 meters = 104 meters
Total Time = Time for uniform velocity + Time for variable velocity
= 8 seconds + 10 seconds = 18 seconds

Average Velocity = 104 meters / 18 seconds = 5.78 m/s

Therefore, the average velocity of the cyclist is 5.78 m/s.

To draw the velocity-time graph, we will have a straight line segment representing the uniform velocity phase (8 m/s) for 8 seconds, followed by another straight line segment representing the deceleration phase from 8 m/s to 0 m/s in 10 seconds.

To answer these questions, we need to understand the concepts of velocity, acceleration, and distance covered.

Before we begin, let's define some variables:
- Initial velocity (u) = 8 m/s (uniform velocity)
- Time (t1) = 8 seconds (time taken to cycle at uniform velocity)
- Time (t2) = 10 seconds (time taken for the cycle to come to rest)
- Final velocity (v2) = 0 m/s (cycle comes to rest)
- Average retardation (a) = ? (i)
- Distance covered with uniform velocity (S1) = ? (ii)
- Distance covered with variable velocity (S2) = ? (iii)
- Average velocity of the cyclist (vavg) = ? (iv)

Now, let's proceed to calculate and find answers for each question:

(i) Average retardation (a):
Since retardation is the opposite of acceleration, and acceleration is the rate of change of velocity with respect to time, we can use the formula:
Acceleration (a) = (v2 - u) / t2

Substituting the values:
a = (0 - 8) / 10
a = -0.8 m/s^2

Therefore, the average retardation is -0.8 m/s^2.

(ii) Distance covered with uniform velocity (S1):
Distance covered is given by the formula:
Distance (S) = Velocity (v) * Time (t)

Substituting the values:
S1 = 8 m/s * 8 s
S1 = 64 meters

Therefore, the distance covered with uniform velocity is 64 meters.

(iii) Distance covered with variable velocity (S2):
To calculate the distance covered with variable velocity, we need to find the change in velocity (Δv) and the time taken (t2).

Change in velocity (Δv) = v2 - u

Substituting the values:
Δv = 0 - 8
Δv = -8 m/s

Now, the average velocity for the time taken to stop (t2) is given by the formula:
Average velocity (vavg2) = (v2 + u) / 2

Substituting the values:
vavg2 = (0 + 8) / 2
vavg2 = 4 m/s

Using the formula for distance:
Distance (S2) = Average velocity (vavg2) * Time (t2)

Substituting the values:
S2 = 4 m/s * 10 s
S2 = 40 meters

Therefore, the distance covered with variable velocity is 40 meters.

(iv) Average velocity of the cyclist (vavg):
To find the average velocity, we need to consider the total distance covered (S1 + S2) and the total time taken (t1 + t2).

Total distance covered = S1 + S2
Total time taken = t1 + t2

Substituting the values:
Total distance covered = 64 + 40
Total time taken = 8 + 10

Average velocity (vavg) = Total distance covered / Total time taken
vavg = (64 + 40) / (8 + 10)
vavg = 104 / 18
vavg ≈ 5.78 m/s

Therefore, the average velocity of the cyclist is approximately 5.78 m/s.

Finally, plot a velocity-time graph with the given information.

You paddle a canoe but you pedal a bicycle. What do you mean by "retardation?"

You will have to draw the graph yourself. If you plot V on the y axis and time on the x axis, you have a horizontal line at V = 8 from t = 0 to t = 8; then the line drops in a slanted straight path to V=0 (the x axis) at t = 18.

ii) 8 * 8 = 64 m
iii) (1/2)*10*8 = 40 m
iv) (64+40)/(10+8) = 5.78 m/s