Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET 202623 AprilMorning Shift
Exam
MHT CET
Year
2026
Date
23 April
Shift
Morning Shift
Subject
Physics
Chapter
Motion in One Dimension

MHT CET 2026 · 23 April · Morning Shift · Physics · Motion in One Dimension

A train accelerates from rest at a constant rate 'p' for some time...

A train accelerates from rest at a constant rate 'p' for some time (attains velocity 'v') and then retards to rest at the constant rate 'q'. If the total distance covered by the train is 's', then the velocity 'v' of the train is

Options

  1. A\left( \left( \dfrac{p+q}{2pq} \right) \times s \right)^{\frac{1}{2}}
  2. B\left( \left( \dfrac{p-q}{2pq} \right) \times s \right)^{\frac{1}{2}}
  3. C\left( \left( \dfrac{2pq}{p+q} \right) \times s \right)^{\frac{1}{2}}
  4. D\left( \left( \dfrac{2pq}{p-q} \right) \times s \right)^{\frac{1}{2}}

Correct answer

C. \left( \left( \dfrac{2pq}{p+q} \right) \times s \right)^{\frac{1}{2}}

Step-by-step solution

Let s1s_1 be the distance covered during acceleration and s2s_2 be the distance covered during retardation.

Using the third equation of motion for the acceleration phase:
v2=u2+2as1v^2 = u^2 + 2as_1
v2=0+2ps1⇒s1=v22pv^2 = 0 + 2ps_1 \Rightarrow s_1 = \dfrac{v^2}{2p}

For the retardation phase:
0=v2−2qs2⇒s2=v22q0 = v^2 - 2qs_2 \Rightarrow s_2 = \dfrac{v^2}{2q}

Total distance s=s1+s2s = s_1 + s_2
s=v22p+v22qs = \dfrac{v^2}{2p} + \dfrac{v^2}{2q}
s=v22(1p+1q)s = \dfrac{v^2}{2} \left( \dfrac{1}{p} + \dfrac{1}{q} \right)
s=v22(p+qpq)s = \dfrac{v^2}{2} \left( \dfrac{p+q}{pq} \right)

Solving for vv:
v2=2pqp+qsv^2 = \dfrac{2pq}{p+q} s
v = \left(\left( \dfrac{2pq}{p+q} \right) \times s \right)^{\dfrac{1}{2}}<br><br>Answer:((2pqp+q)×s)12<br><br>Answer: \left( \left( \dfrac{2pq}{p+q} \right) \times s \right)^{\frac{1}{2}}
Practice Motion in One Dimension on Quantrex Academy →

More from Motion in One Dimension

A vehicle runs on a straight road of length 'L'. It travels half the distance with speed… MHT CET Medical 2026For uniform acceleration in linear motion which of the following is NOT CORRECT ? MHT CET Medical 2026Two cars, P and Q move toward each other, getting 8\ m closer every second. If they move… MHT CET Medical 2026A block is kept on the floor of an elevator at rest. The elevator starts descending with… MHT CET Medical 2026The acceleration (a ) -time (t ) graph for the body starting from rest is as shown in the… MHT CET Medical 2026The following plots show variation of velocity ( v ) with time ( t ), of a ball thrown… NEET 2026Consider a particle moving along a straight line, whose position as a function of time is… NEET 2026When a ruler falls vertically, 5 different persons catch it with different reaction… NEET 2026 Full Motion in One Dimension list All MHT CET Medical PYQs