Martians ships will take 400 years to each earth, but they sent a scout that is to fly by our moon at 0.1x10^8 m/s (velocity). We hide our own scout at the moon, that can accelerate at 6.3x10^3 m/s2. How long will it take us to overtake their scout? How far will the martians have travelled by that time? (straight line path)
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
Martians ships will take 400 years to each earth, but they sent a scout that is to fly by our moon at 0.1x10^8 m/s (velocity). We hide our own scout at the moon, that can accelerate at 6.3x10^3 m/s2. How long will it take us to overtake their scout? How far will the martians have travelled by that time? (straight line path)
It is known that if a body is moving in a constant velocity 'V' for a certain time 't' , then the distance traveled(d) is given by the formula :
d = V.t ......(i)
And if the body starts from rest, and accelerates with an acceleration 'a' for a certain time , then the distance traveled(d') is given by the formula :
d' = (1/2).a.t2 ......(ii)
As given in the question , that one scout overtake the other, this means that they cover a same amount of distance. This implies that equation (i) and (ii) are equal , and this further implies:
V.t = (1/2).a.t2
=> t = (2.V)/a ...... (iii)
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