1st Equation of Motion

Q. Derive formula for the time period of projectile motion.

Q.

Derive the third equation of motion:$v^2-u^2=2as$.

Q. How acceleration due to gravity varies due to rotation of the earth?

Q. A car, moving with a speed of $50km/hr$, can be stopped by brakes after at least $6m$. If the same car is moving at a speed of $100km/hr$, the minimum stopping distance is

1. $20m$
2. $8m$
3. $24m$
4. $22m$

Q.

An automobile moving with a speed 60kmph can break to stop at a distance 20m. A car is moving twice as fast as this, the stopping distance will be?

Q.

If a body loses half of its velocity on penetrating $3cm$ in a wooden block, then how much will it penetrate more before coming to rest?

1. $1cm$

2. $2cm$

3. $3cm$

4. $4cm$

Q.

two balls A and B are thrown simultaneously vertically upwards with a speed of 20 metre per second from the ground and the downwards s from a height of 40m with the same speed and along the same line of motion at what point does the ball collide?

Q.

What does constant acceleration mean?

Q. The relation between time t and displacement is x is t = ax²​​^​​​+bx

​​​​​Where a and b are constants. Find the relation between acceleration and velocity.
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NOTE:I have a word with one of the subject experts named Aldin D Sousa.so, please him give the explanation.
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Q.

A particle is moving on a straight line, where its position is a function of time $t$ given by $s=a{t}^2+bt+6\ge 0$. If it is known that the particle comes to rest after $4seconds$ at a distance of $16metres$ from the starting position $(t=0)$, then the retardation in its motion is

1. $-1m/s^2$

2. $\frac{5}{4}m/s^2$

3. $\frac{1}{2}m/s^2$

4. $-\frac{5}{4}m/s^2$

Q.

A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity vs time?

1. 

2. 

3. 

4. 

Q.

a ball is thrown vertically upwards with velocity of 25 m/s from the top of Tower of height 30m. how long it will take to travel before it hits the ground? g=10m/s^2

Q. A car accelerates from rest at a constant rate of $2m{s}^{-2}$ for some time. Then it retards at a constant rate of $4m{s}^{-2}$ and come to rest. It remains in motion for $6s$.

1. Its maximum speed is $8m{s}^{-1}$
2. It maximum speed is $6m{s}^{-1}$
3. It travelled a total distance of $24m$
4. It travelled a total distance of $18m$

Q.

When a balloon rising vertically upwards at a velocity of 10 m per second is at a height of 45 m from the ground a parachutist bails out from the balloon after 3 second he opens the parachute and deaccelerates at a constant rate of 5 metre per second square then find

1. what is the height of the parachutist above the ground when he opens the parachute.

2. how far is he from the balloon at this instant.

3. with what velocity does he strike the ground.

4. what time does he take in striking the ground after his exit from the balloon.

(take g=10 metre per second square)

Q. What is the SI unit and dimension of surface tension?

Q.

What is the vector product of two parallel vectors?

Q. The energy in $\text{MeV}$ released due to conversion of $1\text{kg}$ mass completely into energy is $(c=3\times {10}^8{\text{ms}}^{-1})$

1. $5.625\times {10}^{29}\text{MeV}$
2. $29\times {10}^5\text{MeV}$
3. $7.625\times {10}^9\text{MeV}$
4. $2.8\times {10}^{15}\text{MeV}$

Q.

A projectile is projected with velocity of 50m/s at an angle of 60^° with the horizontal from the ground. The time after which is velocity will make an angle of 45^° with the horizontal is

1)2.5s

2)1.83s

3)2.37s

4)3.72s

Q. A man is 45m behind the bus, when the bus start accelerating from rest with acceleration $2.5m/s^2$. With what minimum velocity should the man start running to catch the bus?

1. 14 m/s
2. 15 m/s
3. 16 m/s
4. 12 m/s

Q.

The velocity of a body moving with a uniform acceleration of $2m{s}^{-2}$ is $10m{s}^{-1}$. What is its velocity after an interval of $4$ second?

Q.

A ball is dropped from a tower. In the last second of its motion it travels a distance of 15m. Find the height of the tower. (take g = 10 m/s)

Q.

A truck starts from rest and accelerates uniformly at $2.0m{s}^{-2}$. At t = 10 s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 11 s? (Neglect air resistance.)

Q. How to Derive the Parth equation and horizontal range and the time of flight and the maximum height in a projectile motion?

Q.

The angle made by the string of a simple pendulum with the vertical depends on time as $\theta =\frac{\pi }{90}sin\left[\right(\pi s^{-1\left)t\right].}$ Find the length of the pendulum if $g={\pi }^{2}m{s}^{-2}.$

Q. A coin is dropped in a lift. It takes time $t_1$ to reach the floor when lift is stationary. It takes time $t_2$ when lift is moving up with constant acceleration. Then

1. >
2. >
3. =
4. >>

Q. A body is projected vertically upward with speed 40m/s. The distance travelled by body in the last second of upward journey is (take g=9.8m/s and neglect effect of air resistance) (1) 4.9m (2) 9.8m (3) 12.4m (4) 19.6m

Q.

If an object is thrown horizontally with an initial speed 10 M per second from the top of the building of height hundred metre. what is horizontal distance covered by the particle?

Q.

A stone is thrown vertically upward with a speed of 28 m/s.

(a) Find the maximum height reached by the stone.

(b) Find its velocity one second before it reaches the maximum height.

(c) Does the answer of part

(d) Change if the initial speed is more than 28 m/s such as 40 m/s or 80 m/s ?

Q. A body starts from rest with a uniform acceleration. If its velocity after $n$ second is $v$, then its displacement in the last $2\text{s}$ is

1. $\frac{2v(n+1)}{n}$
2. $\frac{v(n+1)}{n}$
3. $\frac{v(n-1)}{n}$
4. $\frac{2v(n-1)}{n}$

Q.

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of

1. $3s$

2. $5s$

3. $7s$

4. $9s$