Match the first column with appropriate entries in the second and third columns and remake the table. S. No. Column 1 Column 2 Column 3 1 Negative acceleration The velocity of the object remains constant A car, initially at rest reaches a velocity of 50 km / hr in 10 seconds 2 Positive acceleration The velocity of the object decreases A vehicle is moving with a velocity of 25 m / s 3 Zero acceleration The velocity of the object increases A vehicle moving with the velocity 10 m / s , stops after 5 seconds

S. No. Column 1 Column 2 Column 3 1 Negative acceleration The velocity of the object decreases A vehicle moving with the velocity 10 m / s , stops after 5 seconds 2 Positive acceleration The velocity of the object increases A car, initially at rest reaches a velocity of 50 km / hr in 10 seconds 3 Zero acceleration The velocity of the object remains constant A vehicle is moving with a velocity of 25 m / s In positive acceleration, velocity of the object increases. In the negative acceleration velocity of the object decreases; the object may still travel in the same direction, but since the final velocity is smaller than the initial velocity, the object's acceleration is negative. Zero acceleration is where the object is moving at a constant velocity relative to an inertial reference frame.

Complete the following table. u ( m / s ) a ( m / s 2 ) t ( sec ) v = u + at ( m / s ) 2 4 3 - - 5 2 20 u ( m / s ) a ( m / s 2 ) t ( sec ) s = ut + 1 2 at 2 ( m ) 5 12 3 - 7 - 4 92 u ( m / s ) a ( m / s 2 ) s ( m ) v 2 = u 2 + 2 as ( m / s ) 2 4 3 - 8 - 5 8 . 4 10

We can solve these by putting the values in the equation of motion. u ( m / s ) a ( m / s 2 ) t ( sec ) v = u + at ( m / s ) 2 4 3 14 10 5 2 20 For the first row, we have to determine the final velocity. v = u + a t ⇒ v = 2 + 4 × 3 = 14 m / s For the second row, we have to determine initial velocity. 20 = u + 5 × 2 ⇒ u = 20 - 10 = 10 m / s u ( m / s ) a ( m / s 2 ) t ( sec ) s = ut + 1 2 at 2 ( m ) 5 12 3 69 7 8 4 92 For the first row, we have to determine the displacement. s = u t + 1 2 a t 2 = 5 × 3 + 1 2 × 12 × ( 3 ) 2 = 69 m For the second row, we have to determine the acceleration. 92 = 7 × 4 + 1 2 × a × ( 4 ) 2 = 28 + 8 a ⇒ a = 64 8 = 8 m / s 2 u ( m / s ) a ( m / s 2 ) s ( m ) v 2 = u 2 + 2 as ( m / s ) 2 4 3 - 1 . 33 8 - 4 , 4 5 8 . 4 100 For the first row, we have to determine the displacement. v 2 = u 2 + 2 a s ⇒ 8 = ( 4 ) 2 + 2 × 3 × s ⇒ s = - 4 3 m = - 1 . 33 m For the second row, we have to determine the initial velocity. 100 = u 2 + 2 × 5 × 8 . 4 ⇒ u 2 = 16 ⇒ u = - 4 ms - 1 , 4 ms - 1

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The ratio of displacement in $n$ second and in the $n^{th}$ second for a particle moving in a straight line under constant acceleration starting from rest is

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Important Questions on Motion

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Science>Physics>Motion>Equations of Motion

Two bodies of masses

m_{a}, m_{b} (m_{a} > m_{b})

are dropped from heights

‘ a ’, ‘ b ’

respectively. The ratio of velocities with which they reach ground is:

MEDIUM

Science>Physics>Motion>Equations of Motion

A stone is dropped into a well having free water surface at depth

44.1 m

. The splash is heard

3.13 \sec

after the stone is dropped. Find the velocity of sound in air (Take

g = 9.8 \frac{m}{s^{2}}

)

EASY

Science>Physics>Motion>Equations of Motion

The initial velocity of a particle is

10 m / s

. It is moving with an acceleration of

4 m / s^{2}

. The distance covered by the particle after

2 s

MEDIUM

Science>Physics>Motion>Equations of Motion

The velocity – time graph of a moving body is shown in the figure. Which of the following statements is true?

Question Image

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Science>Physics>Motion>Equations of Motion

Two steel balls of mass

1 kg

and

2 kg

and a lead ball of

10 kg

are released together from the top of tower

30 m

high. Assuming the path to be in vacuum:

EASY

Science>Physics>Motion>Equations of Motion

A body is travelling with speed

20 m s^{- 1}

having acceleration

4 m s^{- 2}

the speed of the body after

2 s

MEDIUM

Science>Physics>Motion>Equations of Motion

A bus of mass

2800 kg

is travelling at a speed of

90 \frac{km}{h}

. A retarding force of

5600 N

is applied on it for a distance of

100 m

. Its velocity reduces to

HARD

Science>Physics>Motion>Equations of Motion

Three particles A, B and C are thrown from top of a building with same speed. A is thrown upwards, B is thrown downwards and C is thrown horizontally, they hit the ground with speed $V_{A}$ , $V_{B}$ and $V_{C}$ respectively then

EASY

Science>Physics>Motion>Equations of Motion

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S1 and that covered in next 10 seconds is S2 then

MEDIUM

Science>Physics>Motion>Equations of Motion

Which of the following is an equation for position - Time relation?

MEDIUM

Science>Physics>Motion>Equations of Motion

Derive third equation of motion by graphical method.

HARD

Science>Physics>Motion>Equations of Motion

Derive second equation of motion by graphical method.

EASY

Science>Physics>Motion>Equations of Motion

Match the first column with appropriate entries in the second and third columns and remake the table.

S. No.	Column 1	Column 2	Column 3
1	Negative acceleration	The velocity of the object remains constant	A car, initially at rest reaches a velocity of $50 km / hr$ in $10$ seconds
2	Positive acceleration	The velocity of the object decreases	A vehicle is moving with a velocity of $25 m / s$
3	Zero acceleration	The velocity of the object increases	A vehicle moving with the velocity $10 m / s$ , stops after $5$ seconds

MEDIUM

Science>Physics>Motion>Equations of Motion

How will the equations of motion for an object moving with a uniform velocity change?

EASY

Science>Physics>Motion>Equations of Motion

A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of

3.0 {m/s}^{2}

for

8 .0 s .

How far does the boat travel during this time?

MEDIUM

Science>Physics>Motion>Equations of Motion

Complete the following table.

$u (m / s)$	$a (m / s^{2})$	$t (\sec)$	$v = u + at (m / s)$
$2$	$4$	$3$	-
-	$5$	$2$	$20$

$u (m / s)$	$a (m / s^{2})$	$t (\sec)$	$s = ut + \frac{1}{2} {at}^{2} (m)$
$5$	$12$	$3$	-
$7$	-	$4$	$92$

$u (m / s)$	$a (m / s^{2})$	$s (m)$	$v^{2} = u^{2} + 2 as (m / s)^{2}$
$4$	$3$	-	$8$
-	$5$	$8.4$	$10$

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Science>Physics>Motion>Equations of Motion

A car is travelling along the road at

8 m s^{- 1}

. It accelerates at

1 m s^{- 2}

for a distance of

18 m

. How fast is it then travelling?

MEDIUM

Science>Physics>Motion>Equations of Motion

A car is travelling at

20 m s^{- 1}

along a road. A child runs out into the road

50 m

ahead and the car driver steps on the brake pedal. What must the car’s deceleration be if the car is to stop just before it reaches the child?

HARD

Science>Physics>Motion>Equations of Motion

An object starting from rest travels

20 m

in first

2 s

and

160 m

in next

4 s

. What will be the velocity after

7 s

from the start?

MEDIUM

Science>Physics>Motion>Equations of Motion

A car of mass

1000 kg

starts from rest and comes down an inclined slope. If it travels a distance of

300 m in 30

seconds, calculate: (a) acceleration and (b) force acting on car.

The ratio of displacement in n second and in the nth second for a particle moving in a straight line under constant acceleration starting from rest is

Important Questions on Motion

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The ratio of displacement in $n$ second and in the $n^{th}$ second for a particle moving in a straight line under constant acceleration starting from rest is