a car starts from rest at a check point A and comes to rest at the next check point B, 6km away, in 3min it has first a uniform retardation after 20s. sketch a velocity time graph of the motion. find the maximum speed and retardation?
Answer
To sketch the velocity-time graph, we need to first understand the motion of the car. We are given that the car starts from rest (meaning initial velocity, u = 0) at checkpoint A, and comes to rest (meaning final velocity, v = 0) at checkpoint B, which is 6 km away from A. The time taken for this motion is 3 minutes or 180 seconds.
Given that there is a uniform retardation after 20 seconds, we can break down the motion into two parts: the initial acceleration phase (from t = 0 to t = 20) and the uniform retardation phase (from t = 20 to t = 180).
1. Initial acceleration phase (t = 0 to t = 20):
During this phase, the car moves with a uniform acceleration because it starts from rest. Let's denote this acceleration as 'a'. The velocity at any time t during this phase can be calculated using the equation:
v = u + at,
where v is the velocity, u is the initial velocity (0 in this case), a is the acceleration, and t is the time.
2. Uniform retardation phase (t = 20 to t = 180):
After 20 seconds, the car experiences a uniform retardation. Let's denote this retardation as 'b'. The velocity at any time t during this phase can be calculated using the equation:
v = u - bt,
where v is the velocity, u is the initial velocity (the maximum speed obtained during the initial acceleration phase), b is the retardation, and t is the time.
Now, let's find the maximum speed and retardation:
1. Maximum speed:
To find the maximum speed, we need to determine the velocity at the end of the initial acceleration phase (t = 20). We can use the equation mentioned in step 1, where u = 0, and t = 20:
v = 0 + a * 20.
Since this is the maximum speed, we can denote it as 'V_max'.
2. Retardation:
The retardation, denoted as 'b', remains constant during the uniform retardation phase. It can be calculated using the equation mentioned in step 2, where u = V_max, v = 0, and t = (180 - 20):
0 = V_max - b * (180 - 20).
Now that we have calculated V_max and b, we can sketch the velocity-time graph:
- The graph will show an initial positive slope representing the acceleration phase until t = 20.
- After t = 20, the graph will show a negative slope representing the uniform retardation phase until t = 180.
- The final velocity at t = 180 will be zero.
Remember to label the axes (velocity on the y-axis and time on the x-axis) and the crucial points (initial and final velocities).
Note: To find precise values for V_max and b, you would need actual numerical data. The above steps provide the methodology to find these values using equations and assumptions.
To give answer
sketch the velocity ,time graph of the motion
in 3min it has first a uniform retardation after 20s.
what does that even mean?