Answer to Question #118229 in Mechanics | Relativity for Rashika

Question #118229
A bus starts from rest with a constant acceleration of 5 m/sec Square. at the same time a car travelling at a constant velocity of 50m/sec overtakes the Bus and passes it. find at what distance will the bus overtake the car and how fast the bus would be travelling then
Expert's answer

The law of the motion with the constant acceletation (from the origin of the coordinates and from rest):

"x_{bus}(t) = \\dfrac{at^2}{2}"

where "x(t)" is the bus coordinate at time "t".

The law of the car's motion (constant speed, starts from the origin):

"x_{car}(t) = vt"

The time at which the bus will overtake the car satisfies the following consition:

"x_{bus}(t_{overtake}) = x_{car}(t_{overtake})\\\\\n\\dfrac{at_{overtake}^2}{2} = vt_{overtake} \\Rightarrow t_{overtake} = \\dfrac{2v}{a} = \\dfrac{2\\cdot 50}{5} = 20 s"

The distans of the meeting then:

"d = x_{car}(t_{overtake}) = vt_{overtake} = 50\\cdot 20 = 1000 m"

The speed of the bus at that time will be:

"v_{bus} = at_{overtake} = 5\\cdot 20 = 100 m\/s"

Answer. d = 1000 m, v = 100 m/s.

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