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A car is travelling at 20m/s along a road . A child runs out into the road 50m ahead and the car driver steps on the brake pedal . What must be car's deceleration if the car is to stop just before it reaches the child ?
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A car is travelling at 20m/s along a road . A child runs out into the ...
Introduction:
To calculate the required deceleration of a car to stop just before reaching a child who has run out into the road, we need to use the equations of motion and kinematics.
Given data:
- Initial velocity (u) of the car = 20 m/s
- Distance (s) between the car and the child = 50 m
- Final velocity (v) of the car is 0 m/s (as it needs to stop)
Using the equation of motion:
The equation of motion that relates the initial velocity (u), final velocity (v), acceleration (a), and distance (s) is:
v^2 = u^2 + 2as
Step 1: Calculating the initial velocity squared (u^2):
The initial velocity (u) of the car is given as 20 m/s. To calculate the initial velocity squared (u^2), we can use the formula:
u^2 = 20^2 = 400 m^2/s^2
Step 2: Calculating the distance (s):
The distance (s) between the car and the child is given as 50 m.
Step 3: Calculating the final velocity squared (v^2):
The final velocity (v) of the car is given as 0 m/s. To calculate the final velocity squared (v^2), we can use the formula:
v^2 = 0^2 = 0 m^2/s^2
Step 4: Calculating the required deceleration (a):
We can rearrange the equation of motion to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Substituting the known values into the equation:
a = (0 - 400) / (2 * 50)
a = -400 / 100
a = -4 m/s^2 (Note: The negative sign indicates deceleration)
Conclusion:
To stop just before reaching the child, the car must have a deceleration of 4 m/s^2. This means that the car's speed will decrease by 4 m/s every second until it comes to a complete stop. It is important for the driver to react quickly and apply the brakes in order to avoid hitting the child.
To calculate the required deceleration of a car to stop just before reaching a child who has run out into the road, we need to use the equations of motion and kinematics.
Given data:
- Initial velocity (u) of the car = 20 m/s
- Distance (s) between the car and the child = 50 m
- Final velocity (v) of the car is 0 m/s (as it needs to stop)
Using the equation of motion:
The equation of motion that relates the initial velocity (u), final velocity (v), acceleration (a), and distance (s) is:
v^2 = u^2 + 2as
Step 1: Calculating the initial velocity squared (u^2):
The initial velocity (u) of the car is given as 20 m/s. To calculate the initial velocity squared (u^2), we can use the formula:
u^2 = 20^2 = 400 m^2/s^2
Step 2: Calculating the distance (s):
The distance (s) between the car and the child is given as 50 m.
Step 3: Calculating the final velocity squared (v^2):
The final velocity (v) of the car is given as 0 m/s. To calculate the final velocity squared (v^2), we can use the formula:
v^2 = 0^2 = 0 m^2/s^2
Step 4: Calculating the required deceleration (a):
We can rearrange the equation of motion to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Substituting the known values into the equation:
a = (0 - 400) / (2 * 50)
a = -400 / 100
a = -4 m/s^2 (Note: The negative sign indicates deceleration)
Conclusion:
To stop just before reaching the child, the car must have a deceleration of 4 m/s^2. This means that the car's speed will decrease by 4 m/s every second until it comes to a complete stop. It is important for the driver to react quickly and apply the brakes in order to avoid hitting the child.
Community Answer
A car is travelling at 20m/s along a road . A child runs out into the ...
- 4 m/s...
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A car is travelling at 20m/s along a road . A child runs out into the road 50m ahead and the car driver steps on the brake pedal . What must be car's deceleration if the car is to stop just before it reaches the child ?
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A car is travelling at 20m/s along a road . A child runs out into the road 50m ahead and the car driver steps on the brake pedal . What must be car's deceleration if the car is to stop just before it reaches the child ? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A car is travelling at 20m/s along a road . A child runs out into the road 50m ahead and the car driver steps on the brake pedal . What must be car's deceleration if the car is to stop just before it reaches the child ? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car is travelling at 20m/s along a road . A child runs out into the road 50m ahead and the car driver steps on the brake pedal . What must be car's deceleration if the car is to stop just before it reaches the child ?.
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