Rectilinear Motion
We will cover following topics
Rectilinear Motion
Rectilinear motion is another name for straight-line motion. The following four equations hold true for such motion:
- For position of the moving object:
- For final velocity:
- For displacement:
- For final velocity, when time is not given:
PYQs
Rectilinear Motion
1) A particle moves in a straight line. Its acceleration is directed towards a fixed point O in the line and is always equal to μ(a5x2)1/3 when it is at a distance x from O. If it starts from rest at a distance a from O, then find the time the particle will arrive at O.
[2016, 15M]
2) A mass starts from rest at a distance ′a′ from the centre of force which attracts inversely as the distance. Find the time of arriving at the centre.
[2015, 13M]
3) A particle moves with an acceleration
μ(x+a4x3)towards the origin. It it starts from rest at a distance a from the origin, find its velocity when its distance from the origin is a2.
[2012, 12M]
4) The velocity of a train increases from 0 to v at a constant acceleration f1, then remains constant for an interval and again decreases to 0 at a constant retardation f2. If the total distance described is x, find the total time taken.
[2011, 10M]
6) A particle of mass m moves on straight line under an attractive force mn2x towards a point O on the line, where x is the distance from O. If x=a and dxdt=u when t=0, find x(t) for any time t>0.
[2011, 10M]
7) After a ball has been falling under gravity for 5 seconds, it passes through a plane of glass and loses half its velocity. If it now reaches the ground in 1 second, find the height of glass above the ground.
[2011, 10M]
8) A particle falls from rest under gravity in a medium whose resistance varies as the velocity of the particle. Find the distance fallen by the particle and its velocity at time t.
[2007, 12M]
9) A particle, whose mass is m, is acted upon by a force m(x+a4x3) towards the origin. If it starts from rest at a distance a, show that it will arrive at origin in time π4.
[2006, 15M]
10) A point moving with uniform acceleration describes distances s1$and$s2 metres in successive intervals of time t1 and t2 seconds. Express the acceleration in terms of s1, s2, t1 and t2.
[2004, 12M]
11) A particle of mass m is acted upon by a force m(x+a4x3) towards the origin. If it starts from rest at a distance a from the origin, show that the time taken by it to reach the origin is π/4.
[2002, 12M]