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

A bus is moving at a speed of 36 km h . It is retarding at a rate of 4 m s 2 and comes to rest finally. Find the distance travelled by it.

Given that, Initial velocity of the bus, u = 36 km h = 36 × 1000 3600 = 10 m s , As the bus comes to rest, its final velocity, v = 0 m s , The acceleration of the bus, a = - 4 m s 2 , ...(Negative sign shows retardation) Let s be the distance travelled by bus before coming to rest. We know that, by the third equation of motion, v 2 - u 2 = 2 a s , Putting all the given values in the above equation, ⇒ 0 2 - 10 2 = 2 × ( - 4 ) × s ⇒ s = ( - 100 ) 2 × ( - 4 ) ⇒ s = 12 . 5 m . Thus, the distance travelled by a bus before coming to rest is s = 12 . 5 m .

HARD

Earn 100

A spacecraft is flying in a straight path and it has a velocity of $100 km s^{- 1}$ fires its rocket motors for $8.0 s$ . At the end of this time, its velocity increases and becomes $140 km s^{- 1}$ Find the distance travelled by the spacecraft in the first $12 s$ after the motors were started? The motors were in action for only $8.0 s$ .

Important Questions on Motion

MEDIUM

Science>Physics>Motion>Equations of Motion

A body is dropped from rest. Its velocity varies with displacement covered as:

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

EASY

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

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:

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

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

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

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?

HARD

Science>Physics>Motion>Equations of Motion

A ball is thrown vertically upwards with a velocity of

49 m / s

. Calculate (Take

g = 9.8 m / s^{2}

)
(i) the maximum height to which it rises,
(ii) the total time it takes to return to the surface of the earth.

MEDIUM

Science>Physics>Motion>Equations of Motion

The average resisting force that must act on a

5 kg

mass to reduce its speed from

65 cm s^{- 1}

0.15 cm s^{- 1}

with a time of

0.2 s

EASY

Science>Physics>Motion>Equations of Motion

A body is projected vertically upward direction with a speed $u$ . Find the (a) time taken (b) distance travelled by the body in reaching its topmost point.

MEDIUM

Science>Physics>Motion>Equations of Motion

Two stones of masses in the ratio of