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A car is moving with speed 30m/sec on a circular path of radius 500m. Its speed is increasind at the rate of 2m/sec^2 . What is the accelearation of the car at that moment ?
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A car is moving with speed 30m/sec on a circular path of radius 500m. ...
Given:
- Speed of the car (v) = 30 m/s
- Radius of circular path (r) = 500 m
- Rate of increase in speed (dv/dt) = 2 m/s²
To Find:
- Acceleration of the car (a)
Explanation:
The acceleration of an object moving in a circular path is given by the formula:
a = v² / r
Step 1: Calculate the initial velocity (u) of the car using the formula:
v = u + at
Given that the initial velocity (u) is 0 (as the car starts from rest), we can rearrange the equation to solve for time (t):
t = v / a
Substituting the values, we get:
t = 30 m/s / 2 m/s² = 15 seconds
Step 2: Calculate the initial acceleration (a) of the car using the formula:
a = (v - u) / t
Substituting the values, we get:
a = (30 m/s - 0) / 15 s = 2 m/s²
Step 3: Calculate the final velocity (v') of the car using the formula:
v' = v + at
Substituting the values, we get:
v' = 30 m/s + (2 m/s²)(15 s) = 60 m/s
Step 4: Calculate the acceleration (a') of the car at that moment using the formula:
a' = (v' - v) / t
Substituting the values, we get:
a' = (60 m/s - 30 m/s) / 15 s = 2 m/s²
Conclusion:
The acceleration of the car at that moment is 2 m/s².
- Speed of the car (v) = 30 m/s
- Radius of circular path (r) = 500 m
- Rate of increase in speed (dv/dt) = 2 m/s²
To Find:
- Acceleration of the car (a)
Explanation:
The acceleration of an object moving in a circular path is given by the formula:
a = v² / r
Step 1: Calculate the initial velocity (u) of the car using the formula:
v = u + at
Given that the initial velocity (u) is 0 (as the car starts from rest), we can rearrange the equation to solve for time (t):
t = v / a
Substituting the values, we get:
t = 30 m/s / 2 m/s² = 15 seconds
Step 2: Calculate the initial acceleration (a) of the car using the formula:
a = (v - u) / t
Substituting the values, we get:
a = (30 m/s - 0) / 15 s = 2 m/s²
Step 3: Calculate the final velocity (v') of the car using the formula:
v' = v + at
Substituting the values, we get:
v' = 30 m/s + (2 m/s²)(15 s) = 60 m/s
Step 4: Calculate the acceleration (a') of the car at that moment using the formula:
a' = (v' - v) / t
Substituting the values, we get:
a' = (60 m/s - 30 m/s) / 15 s = 2 m/s²
Conclusion:
The acceleration of the car at that moment is 2 m/s².
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A car is moving with speed 30m/sec on a circular path of radius 500m. Its speed is increasind at the rate of 2m/sec^2 . What is the accelearation of the car at that moment ?
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A car is moving with speed 30m/sec on a circular path of radius 500m. Its speed is increasind at the rate of 2m/sec^2 . What is the accelearation of the car at that moment ? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A car is moving with speed 30m/sec on a circular path of radius 500m. Its speed is increasind at the rate of 2m/sec^2 . What is the accelearation of the car at that moment ? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car is moving with speed 30m/sec on a circular path of radius 500m. Its speed is increasind at the rate of 2m/sec^2 . What is the accelearation of the car at that moment ?.
A car is moving with speed 30m/sec on a circular path of radius 500m. Its speed is increasind at the rate of 2m/sec^2 . What is the accelearation of the car at that moment ? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A car is moving with speed 30m/sec on a circular path of radius 500m. Its speed is increasind at the rate of 2m/sec^2 . What is the accelearation of the car at that moment ? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car is moving with speed 30m/sec on a circular path of radius 500m. Its speed is increasind at the rate of 2m/sec^2 . What is the accelearation of the car at that moment ?.
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