A CAR STARTS FROM REST AT A CHECKPOINT A AND COMES TO REST AT THE NEXT CHECKPOINT B,6KM AWAY IN 3 MINUTES.IT HAS FIRST A UNIFORM ACCELERATION FOR 40 SECONDS,THEN A CONSTANT SPEED AND IS BROUGHT TO REST WITH A UNIFORM RETARDATION AFTER 20 SECONDS.SKETCH A VELOCITY-TIME GRAPH OF THE MOTION.DETERMINE MAXIMUM SPEED AND RETARDATION.
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To sketch the velocity-time graph and determine the maximum speed and retardation, we can break down the motion into different phases.
Phase 1: Acceleration (Uniform)
The car starts from rest at checkpoint A and undergoes a uniform acceleration for 40 seconds. Let's denote this time as t1.
To determine the acceleration, we can use the formula:
v = u + at
Since the car starts from rest (u = 0), the equation simplifies to:
v = at
The distance covered during this phase can be calculated using the formula:
s = ut + (1/2)at^2
Given that the distance covered in this phase is 6 km, we can substitute the known values:
6 = 0 + (1/2)at1^2
Phase 2: Constant speed
After 40 seconds, the car maintains a constant speed until it reaches the next checkpoint B, 6 km away, in 3 minutes (180 seconds).
To calculate the speed during this phase, we can use the formula:
v = s/t
Since the distance covered is 6 km and the time taken is 180 seconds, we have:
v = 6/180
Phase 3: Retardation (Uniform)
The car is brought to rest after 20 seconds with a uniform retardation. Let's denote this time as t3.
Using the formula from phase 1, we can determine the speed at the end of phase 2 as the initial speed for this phase.
The distance covered during this phase can be calculated using the formula:
s = ut + (1/2)at^2
Since the final speed is 0, the equation simplifies to:
0 = v2 + at3
Now, let's summarize the phases and calculate the values.
Phase 1: Uniform acceleration (t1 = 40 seconds)
- Calculate 'a' using the equation: 6 = (1/2)a(40)^2
- Calculate 'v1' using the equation: v1 = a(40)
Phase 2: Constant speed (t2 = 180 seconds)
- Calculate constant speed using the equation: v2 = 6/180
Phase 3: Uniform retardation (t3 = 20 seconds)
- Calculate 'a' using the equation: 0 = v2 + a(20)
Once we have calculated the values, we can plot the velocity-time graph with time along the x-axis and velocity along the y-axis. The graph will have three phases: an increasing line segment (phase 1), a horizontal line segment at a constant value (phase 2), and a decreasing line segment (phase 3).
The maximum speed can be found by determining the highest point on the graph, and the retardation can be determined by calculating the negative value of the slope of the decreasing line segment.
Please provide the values for 'a', 'v1', 'v2' obtained from the above calculations, and I can help you sketch the velocity-time graph and determine the maximum speed and retardation.