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A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 19.0m/s , and the distance between them is 52.0m . After t1 = 5.00s , the motorcycle starts to accelerate at a rate of 5.00m/s^2. a. How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words. b. Find t2−t1

Respuesta :

Answer:

[tex]t\approx4.561\ s[/tex]

Explanation:

Given:

  • initial speed of car and motorcycle, [tex]v=19\ m.s^{-1}[/tex]
  • initial distance between the car and motorcycle, [tex]s=52\ m[/tex]
  • time after which the motorcycle starts to accelerate, [tex]t_1=5\ s[/tex]
  • rate of acceleration of motorcycle, [tex]a=5\ m.s^{-2}[/tex]

The initially the relative velocity of the motorcycle is zero with respect to car.

Now using the equation of motion in the relative quantities:

[tex]s=u.t+\frac{1}{2} .a.t^2[/tex]

here:

[tex]s =[/tex] relative distance of motorcycle with respect to the car

[tex]u=[/tex] initial relative velocity of the motorcycle with respect to the car

[tex]t=[/tex] time taken to cover the distance gap from the car.

[tex]52=0+0.5\times 5\times t^2[/tex]

[tex]t\approx4.561\ s[/tex]

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