Concept explainers
(a)
To Plot: The position vs time graph for both car’s start to the catchup point.
(a)
Explanation of Solution
Given:
Initial speed of police car,
Constant speed of speeder,
Formula used:
Second equation of
Calculation:
Position vs time graph of speeder:
Speeder is moving with constant speed; therefore, it has zero acceleration.
From equation (i):
Distance covered by speeder is directly proportional to the time. Therefore, the plot:
Position vs time graph of police car:
Police car start from the rest, to catch the speeder the police car needs to get accelerated.
From equation (i):
Position of police car is directly proportional to the square of the time, therefore the plot between position and time would be parabola.
Conclusion:
Hence, the position vs time plot of speed would be straight line while the position vs time plot of police car would be parabola.
(b)
To Find: The time taken by police car to overtake the speeder.
(b)
Answer to Problem 77GP
Explanation of Solution
Given:
Initial speed of police car,
Constant speed of speeder,
Distance travelled,
Acceleration of the speeder,
Formula used:
Second equation of kinematics:
Calculation:
Let the time taken by the police car be
From equation (i):
Conclusion:
Time taken by the police car to overtake the speeder:
(c)
To Find: The acceleration of the police car.
(c)
Answer to Problem 77GP
Explanation of Solution
Given:
Initial speed of police car,
Distance travelled by the police car,
Time taken to catch the speeder,
Formula used:
Second equation of kinematics:
Where,
Calculation:
Let the acceleration of the police car be
Plugging in the given values in formula:
Conclusion:
Acceleration of the police car:
(d)
To Find: The speed of police car at the overtaking point.
(d)
Answer to Problem 77GP
Explanation of Solution
Given:
Initial speed of police car,
Time taken to catch the speeder,
Acceleration of the police car,
Formula used:
First equation of kinematics:
Where,
Calculation:
Plugging in the given values in the formula:
Conclusion:
Speed of car at the overtaking point:
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Physics: Principles with Applications
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