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A car start from rest and has an acceleration a=t. A truck is moving with a uniform velocity of 6 m/s. At what distance will the car overtake the truck.( at t=0 both start their motion).?
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A car start from rest and has an acceleration a=t. A truck is moving w...
Problem Overview
At time t=0, a car starts from rest with an acceleration that varies with time, while a truck moves at a constant speed. To find the distance at which the car overtakes the truck, we need to analyze their motions.
Car's Motion
- The car starts from rest, so its initial velocity (u) = 0.
- The acceleration (a) of the car is given as a = t (where t is time in seconds).
- Using the formula for displacement with variable acceleration, we find the distance (s) covered by the car:
- The acceleration is integrated to find velocity:
v = ∫(t dt) = (1/2)t² + C (C=0, since initial velocity is 0)
- Thus, v = (1/2)t².
- Now, integrating the velocity to find displacement:
s_car = ∫((1/2)t² dt) = (1/6)t³.
Truck's Motion
- The truck moves at a uniform velocity of 6 m/s.
- The distance covered by the truck after time t is given by:
s_truck = velocity × time = 6t.
Setting the Distances Equal
To find when the car overtakes the truck, set the distances equal:
- (1/6)t³ = 6t.
Solving the Equation
- Rearranging gives:
t³ - 36t = 0.
Factor out t:
t(t² - 36) = 0.
- Solutions:
t = 0 (initial position) or t² = 36 → t = 6 seconds.
Finding the Distance
- Substitute t = 6 seconds into either distance equation:
s_truck = 6 × 6 = 36 meters.
s_car = (1/6)(6)³ = 36 meters.
Conclusion
The car overtakes the truck at a distance of 36 meters from the starting point after 6 seconds.
At time t=0, a car starts from rest with an acceleration that varies with time, while a truck moves at a constant speed. To find the distance at which the car overtakes the truck, we need to analyze their motions.
Car's Motion
- The car starts from rest, so its initial velocity (u) = 0.
- The acceleration (a) of the car is given as a = t (where t is time in seconds).
- Using the formula for displacement with variable acceleration, we find the distance (s) covered by the car:
- The acceleration is integrated to find velocity:
v = ∫(t dt) = (1/2)t² + C (C=0, since initial velocity is 0)
- Thus, v = (1/2)t².
- Now, integrating the velocity to find displacement:
s_car = ∫((1/2)t² dt) = (1/6)t³.
Truck's Motion
- The truck moves at a uniform velocity of 6 m/s.
- The distance covered by the truck after time t is given by:
s_truck = velocity × time = 6t.
Setting the Distances Equal
To find when the car overtakes the truck, set the distances equal:
- (1/6)t³ = 6t.
Solving the Equation
- Rearranging gives:
t³ - 36t = 0.
Factor out t:
t(t² - 36) = 0.
- Solutions:
t = 0 (initial position) or t² = 36 → t = 6 seconds.
Finding the Distance
- Substitute t = 6 seconds into either distance equation:
s_truck = 6 × 6 = 36 meters.
s_car = (1/6)(6)³ = 36 meters.
Conclusion
The car overtakes the truck at a distance of 36 meters from the starting point after 6 seconds.
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A car start from rest and has an acceleration a=t. A truck is moving with a uniform velocity of 6 m/s. At what distance will the car overtake the truck.( at t=0 both start their motion).?
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A car start from rest and has an acceleration a=t. A truck is moving with a uniform velocity of 6 m/s. At what distance will the car overtake the truck.( at t=0 both start their motion).? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A car start from rest and has an acceleration a=t. A truck is moving with a uniform velocity of 6 m/s. At what distance will the car overtake the truck.( at t=0 both start their motion).? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car start from rest and has an acceleration a=t. A truck is moving with a uniform velocity of 6 m/s. At what distance will the car overtake the truck.( at t=0 both start their motion).?.
A car start from rest and has an acceleration a=t. A truck is moving with a uniform velocity of 6 m/s. At what distance will the car overtake the truck.( at t=0 both start their motion).? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A car start from rest and has an acceleration a=t. A truck is moving with a uniform velocity of 6 m/s. At what distance will the car overtake the truck.( at t=0 both start their motion).? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car start from rest and has an acceleration a=t. A truck is moving with a uniform velocity of 6 m/s. At what distance will the car overtake the truck.( at t=0 both start their motion).?.
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