157- Train A, with length 200 m, is moving at constant speed $4\,\dfrac{\text{m}}{\text{s}}$. Train B, with length 225 m, has stopped on the adjacent track. At the moment train A completely passes train B, train B starts moving in the same direction as train A with constant acceleration $2\,\dfrac{\text{m}}{\text{s}^2}$ and brings its speed up to $50\,\dfrac{\text{m}}{\text{s}}$ and continues at that speed. How many seconds after the start of motion does train B completely pass train A?
(1) $57.5$ (2) $82.5$ (3) $80$ (4) $105$

45. On a straight path, starting from a point, object A moves with constant acceleration $a$ from rest, and at $t = 2\,\mathrm{s}$, object B starts from the same point and moves with constant acceleration $a = 0.5\,\dfrac{\mathrm{m}}{\mathrm{s}^2}$ from rest. If at $t = 6\,\mathrm{s}$ the two objects meet each other, what is their distance at $t = 10\,\mathrm{s}$ in meters?
(1) $4.4$ (2) $8.8$ (3) $13.2$ (4) $24.8$

46. A bullet is released from a point 100 meters above the ground. One second later, another bullet is released from the same point. At the moment the first bullet reaches the ground, what change does the distance between the two bullets undergo? (Assume air resistance is negligible.)
(1) remains constant. (2) increases.
(3) decreases. (4) first decreases and then increases.
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47. Car A moves at a constant speed of $8\,\dfrac{\text{m}}{\text{s}}$ along a straight path, and car B moves behind it at a constant speed of $20\,\dfrac{\text{m}}{\text{s}}$ in the same direction. When the distance between them decreases to 46 meters, car A begins to decelerate with a constant acceleration of $2\,\dfrac{\text{m}}{\text{s}^2}$ and simultaneously car B also decelerates with a constant acceleration of $4\,\dfrac{\text{m}}{\text{s}^2}$. What is the speed of car B at the moment it reaches car A, in meters per second?
(1) $2$ (2) $8$ (3) $4$ (4) $6$

Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f'$ respectively. If $A$ takes $m$ sec. more than $B$ and describes '$n$' units more than $B$ in acquiring the same speed then
(1) $\left(f - f'\right)m^2 = ff'n$
(2) $\left(f + f'\right)m^2 = ff'n$
(3) $\frac{1}{2}\left(f + f'\right)m = ff'n^2$
(4) $\left(f' - f\right)n = \frac{1}{2}ff'm^2$

A body is at rest at $x = 0$. At $t = 0$, it starts moving in the positive $x$-direction with a constant acceleration. At the same instant another body passes through $x = 0$ moving in the positive $x$ direction with a constant speed. The position of the first body is given by $\mathrm { x } _ { 1 } ( \mathrm { t } )$ after time ' t ' and that of the second body by $x _ { 2 } ( t )$ after the same time interval. Which of the following graphs correctly describes $\left( x _ { 1 } - x _ { 2 } \right)$ as a function of time ' $t$ '?
(1), (2), (3), (4) [see graphs in original]

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration $2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ and the car has acceleration $4 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. The car will catch up with the bus after time :
(1) $\sqrt { 120 } \mathrm {~s}$
(2) 15 s
(3) $\sqrt { 110 } \mathrm {~s}$
(4) $10 \sqrt { 2 } \mathrm {~s}$

A ball is projected vertically upward with an initial velocity of $50 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at $t = 0 \mathrm {~s}$. At $t = 2 \mathrm {~s}$, another ball is projected vertically upward with same velocity. At $t =$ $\_\_\_\_$ s, second ball will meet the first ball $\left( \mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 } \right)$.

Two balls $A$ and $B$ are placed at the top of 180 m tall tower. Ball $A$ is released from the top at $t = 0 \mathrm {~s}$. Ball $B$ is thrown vertically down with an initial velocity $u$ at $t = 2 \mathrm {~s}$. After a certain time, both balls meet 100 m above the ground. Find the value of $u$ in $\mathrm { m } \mathrm { s } ^ { - 1 }$. [use $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$]
(1) 10
(2) 15
(3) 20
(4) 30