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A motorist is driving at 80 km/hr on the curved position of a highway of 400m radius. He suddenly applies the brakes and that causes the speed to decrease to 45 km/hr at constant rate in 8 seconds. Determine the tangential and normal components of acceleration immediately after the application of brakes and 4 seconds later.?
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A motorist is driving at 80 km/hr on the curved position of a highway ...
Solution:
Given:
Velocity before braking, V1 = 80 km/hr
Velocity after braking, V2 = 45 km/hr
Radius of the curved road, r = 400 m
Time for which brakes are applied, t = 8 seconds
To find:
Tangential and Normal components of acceleration immediately after the application of brakes and 4 seconds later.
1. Tangential Acceleration:
The tangential acceleration is the rate of change of tangential velocity with respect to time and is given by:
aT = (V2 - V1) / t
Substituting the given values, we get:
aT = (45 - 80) / 8
aT = -4.375 m/s^2
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.
2. Normal Acceleration:
The normal acceleration is the rate of change of direction of velocity with respect to time and is given by:
aN = V^2 / r
where V is the velocity of the vehicle and r is the radius of curvature of the road.
Substituting the given values, we get:
V = 80 km/hr = 22.22 m/s
r = 400 m
aN = (22.22)^2 / 400
aN = 1.23 m/s^2
The normal acceleration is always perpendicular to the tangential acceleration and towards the center of curvature.
3. Tangential and Normal Acceleration after 4 seconds:
After 4 seconds, the velocity of the vehicle would have decreased further. Let us calculate the tangential and normal accelerations at this time.
Using the formula for uniformly accelerated motion:
V2 = V1 + aT*t
45 km/hr = 80 km/hr + aT*4 seconds
aT = -8.75 m/s^2
Using the formula for centripetal acceleration:
aN = V^2 / r
V = 45 km/hr = 12.5 m/s
aN = (12.5)^2 / 400
aN = 0.39 m/s^2
The tangential acceleration is negative and higher in magnitude than before, indicating that the rate of decrease in velocity has increased. The normal acceleration has decreased in magnitude, indicating that the vehicle is taking a wider turn.
Given:
Velocity before braking, V1 = 80 km/hr
Velocity after braking, V2 = 45 km/hr
Radius of the curved road, r = 400 m
Time for which brakes are applied, t = 8 seconds
To find:
Tangential and Normal components of acceleration immediately after the application of brakes and 4 seconds later.
1. Tangential Acceleration:
The tangential acceleration is the rate of change of tangential velocity with respect to time and is given by:
aT = (V2 - V1) / t
Substituting the given values, we get:
aT = (45 - 80) / 8
aT = -4.375 m/s^2
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.
2. Normal Acceleration:
The normal acceleration is the rate of change of direction of velocity with respect to time and is given by:
aN = V^2 / r
where V is the velocity of the vehicle and r is the radius of curvature of the road.
Substituting the given values, we get:
V = 80 km/hr = 22.22 m/s
r = 400 m
aN = (22.22)^2 / 400
aN = 1.23 m/s^2
The normal acceleration is always perpendicular to the tangential acceleration and towards the center of curvature.
3. Tangential and Normal Acceleration after 4 seconds:
After 4 seconds, the velocity of the vehicle would have decreased further. Let us calculate the tangential and normal accelerations at this time.
Using the formula for uniformly accelerated motion:
V2 = V1 + aT*t
45 km/hr = 80 km/hr + aT*4 seconds
aT = -8.75 m/s^2
Using the formula for centripetal acceleration:
aN = V^2 / r
V = 45 km/hr = 12.5 m/s
aN = (12.5)^2 / 400
aN = 0.39 m/s^2
The tangential acceleration is negative and higher in magnitude than before, indicating that the rate of decrease in velocity has increased. The normal acceleration has decreased in magnitude, indicating that the vehicle is taking a wider turn.
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A motorist is driving at 80 km/hr on the curved position of a highway of 400m radius. He suddenly applies the brakes and that causes the speed to decrease to 45 km/hr at constant rate in 8 seconds. Determine the tangential and normal components of acceleration immediately after the application of brakes and 4 seconds later.?
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A motorist is driving at 80 km/hr on the curved position of a highway of 400m radius. He suddenly applies the brakes and that causes the speed to decrease to 45 km/hr at constant rate in 8 seconds. Determine the tangential and normal components of acceleration immediately after the application of brakes and 4 seconds later.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A motorist is driving at 80 km/hr on the curved position of a highway of 400m radius. He suddenly applies the brakes and that causes the speed to decrease to 45 km/hr at constant rate in 8 seconds. Determine the tangential and normal components of acceleration immediately after the application of brakes and 4 seconds later.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A motorist is driving at 80 km/hr on the curved position of a highway of 400m radius. He suddenly applies the brakes and that causes the speed to decrease to 45 km/hr at constant rate in 8 seconds. Determine the tangential and normal components of acceleration immediately after the application of brakes and 4 seconds later.?.
A motorist is driving at 80 km/hr on the curved position of a highway of 400m radius. He suddenly applies the brakes and that causes the speed to decrease to 45 km/hr at constant rate in 8 seconds. Determine the tangential and normal components of acceleration immediately after the application of brakes and 4 seconds later.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A motorist is driving at 80 km/hr on the curved position of a highway of 400m radius. He suddenly applies the brakes and that causes the speed to decrease to 45 km/hr at constant rate in 8 seconds. Determine the tangential and normal components of acceleration immediately after the application of brakes and 4 seconds later.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A motorist is driving at 80 km/hr on the curved position of a highway of 400m radius. He suddenly applies the brakes and that causes the speed to decrease to 45 km/hr at constant rate in 8 seconds. Determine the tangential and normal components of acceleration immediately after the application of brakes and 4 seconds later.?.
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