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A car starts from rest and has an acceleration a=√t . A truck is moving with uniform velocity of 4 m/s . At what distance will be the car overtake the truck ? (At t=0 both start their motion in the same direction from same position)?
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A car starts from rest and has an acceleration a=√t . A truck is movin...
Problem

A car starts from rest and has an acceleration a=√t. A truck is moving with uniform velocity of 4 m/s. At what distance will be the car overtake the truck ? (At t=0 both start their motion in the same direction from same position)?


Solution

Let's first find the equation of motion for the car:


  • Initial velocity of the car, u = 0

  • Acceleration of the car, a = √t

  • Using the equation of motion, s = ut + 1/2 at^2, we get:

  • s = 1/2 (√t) t^2 = 1/2 t^(5/2)


Now, let's find the time it takes for the car to overtake the truck:


  • Let the time taken by the car to overtake the truck be t_o

  • Distance covered by the truck in time t_o, S_t = 4t_o

  • Distance covered by the car in time t_o, S_c = 1/2 t_o^(5/2)

  • At the point of overtaking, both the truck and the car will cover the same distance:

  • S_t = S_c

  • 4t_o = 1/2 t_o^(5/2)

  • Solving for t_o, we get t_o = 16/25 s


Finally, let's find the distance at which the car overtakes the truck:


  • Using the equation of motion for the car, s = 1/2 t^(5/2), we get:

  • s = 1/2 (16/25)^(5/2) = 0.8 m


Therefore, the car will overtake the truck at a distance of 0.8 m.
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A car starts from rest and has an acceleration a=√t . A truck is movin...
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A car starts from rest and has an acceleration a=√t . A truck is moving with uniform velocity of 4 m/s . At what distance will be the car overtake the truck ? (At t=0 both start their motion in the same direction from same position)?
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A car starts from rest and has an acceleration a=√t . A truck is moving with uniform velocity of 4 m/s . At what distance will be the car overtake the truck ? (At t=0 both start their motion in the same direction from same position)? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A car starts from rest and has an acceleration a=√t . A truck is moving with uniform velocity of 4 m/s . At what distance will be the car overtake the truck ? (At t=0 both start their motion in the same direction from same position)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A car starts from rest and has an acceleration a=√t . A truck is moving with uniform velocity of 4 m/s . At what distance will be the car overtake the truck ? (At t=0 both start their motion in the same direction from same position)?.
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