# Magnitude of Instantaneous Velocity

## Trending Questions

**Q.**Two cars P and Q starts from a point at the same time in a straight line and their positions are represented by xp(t)=at+bt2 and xQ(t)=ftâˆ’t2. At what time do the cars have the same velocity?

- fâˆ’a2(1+b)
- aâˆ’f1+b
- a+f2(bâˆ’1)

a+f2(1+b)

**Q.**The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = (8t - 5t2)

meter and x=6t meter, where t is in second. The velocity with which the projectile is projected is

- 6 m/sec
- Not obtainable from the data
- 8 m/sec
- 10 m/sec

**Q.**Velocity of a particle is →v=6^i+2^j−2^k. The component of the velocity parallel to vector a=^i+^j−^k in vector form is

- 6^i+2^j+2^k
- ^i+^j+^k
- 2^i+2^j+2^k
- 6^i+2^j−2^k

**Q.**Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by XP(t)=αt+βt2 and XQ(t)=ft−t2. At what time, both the buses have same velocity?

**Q.**Two projectiles are fired from the two imaginary planets A and B. The projectile is fired from the planet A with a velocity of 10 m/s and at angle θ with horizontal. Another projectile is fired from the surface of planet B with a velocity of 6 m/s at the same angle follows trajectory which is identical with the trajectory of projectile from planet A. What is the ratio of the acceleration due to gravity of planet A to planet B?

- 53
- 35
- 259
- 925

**Q.**The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y=(8t−5t2) meter and x = 6t meter, where t is in second. The velocity with which the projectile is projected is

- 8m/sec
- 6m/sec
- 10m/sec
- Not obtainable from the data.

**Q.**

A body is projected with an initial velocity of (5 ^i + 8 ^j) m/s. The range of the projectile (g = 10 m / s2)

8 m

30 m

10 m

20 m

**Q.**Find the velocity of a projectile at the highest point, if it is projected with a speed 15ms−2, in the direction 45∘ above horizontal.

[take g=10ms−2]

**Q.**A projectile is fired horizontally with a velocity of 98m/s from the top of a hill 490m high. Find the horizontal range of the projectile.

**Q.**The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = (8t - 5t2)

meter and x=6t meter, where t is in second. The velocity with which the projectile is projected is

- 8 m/sec
- 6 m/sec
- 10 m/sec
- Not obtainable from the data

**Q.**The vertical height y and horizontal distance x of a projectile on a certain planet are given by x=(3t) m, y=(4t) m where t is in seconds. Find the speed of projection (in m/s) ?

**Q.**A particle is moving in x−y plane on a straight line its x and y coordinates are given as x=(2t2+4)m and Y=(√3x2+8)m and t is in second. The acceleration of the particle is

- √7m/s2
- √5m/s2
- 2√7m/s2
- None of these

**Q.**

The coordinates of a moving particle at any time are given by x=a t2 and y=b t2. The speed of the particle at any moment is

**Q.**The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y=(8t−5t2) m and x=6tm, where t is in seconds. The velocity with which the projectile is projected at t = 0 is:

- 8ms−1
- 6ms−1
- 10ms−1
- Not obtainable from the data

**Q.**A body changes direction by an angle a, without changing speed (v). Change in magnitude of velocity is

- zero
- 2v sin a/2
- v sin a/2
- v sin a

**Q.**The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = (8t - 5t2)

meter and x=6t meter, where t is in second. The velocity with which the projectile is projected is

- 8 m/sec
- 6 m/sec
- 10 m/sec
- Not obtainable from the data

**Q.**Two swimmers start from point P on one bank of the river to reach Q

*on the opposite bank. Velocity of each swimmer in still waters is 2.5kmh−1. One of the swimmers crosses the river along the straight route PQ*

*and the other swims right angles to the stream and then walks the distance which he has been carried away by the river to get to point Q. Stream velocity is 2kmh−1. If both the swimmers reach point Q simultaneously, the velocity of walking of second swimmer is*

- 3kmh−1
- 4kmh−1
- 2kmh−1
- 3.5kmh−1

**Q.**A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by (4t3−2t). Where t is in second and velocity is in m/s. What is acceleration of the particle, when it is at distance 2m from the origin.

- 28m/s2
- 22m/s2
- 12m/s2
- 10m/s2

**Q.**A jet plane flying at a constant velocity v at a height = 8 km is tracked by a radar R located at O directly below the line of flight. If angle θ is decreasing at rate of 0.025 rad/s velocity of plane when θ = 60∘ is

1440 km/h

960 km/h

1920 km/h

480 km/h

**Q.**

The coordinates of a moving particle at any time are given by x=a t2 and y=b t2. The speed of the particle at any moment is

2t(a + b)

2t√(a2−b2)

t√(a2+b2)

2t√(a2+b2)

**Q.**A jet plane flying at a constant velocity v at a height=8 km is tracked by a radar R located at O directly below the line of flight. If angle θ is decreasing at rate of 0.025 rad/s, the velocity of plane when θ=60∘ is

1440 km/h

960 km/h

1920 km/h

480 km/h

**Q.**A particle is moving on a circular path of radius r with uniform speed V. The magnitude of change in velocity when the particle moves from P to Q is :- (∠PPOQ=40o)

- 2vcos40o
- 2vsin40o
- 2vsin20o
- 2vcos20o

**Q.**

The coordinates of a moving particle at any time are given by x=a t2 and y=b t2. The speed of the particle at any moment is

2t(a + b)

2t√(a2−b2)

t√(a2+b2)

2t√(a2+b2)

**Q.**Two cars P and Q starts from a point at the same time in a straight line and their positions are represented by xp(t)=at+bt2 and xQ(t)=ft−t2. At what time do the cars have the same velocity?

- f−a2(1+b)
- a−f1+b
- a+f2(b−1)

a+f2(1+b)

**Q.**A spaceship approaches the Moon along a parabolic trajectory which is almost tangent to the Moon's surface. At the moment of the maximum approach the brake rocket was fired for a short time interval, and the spaceship was transferred into a circular orbit of a Moon satellite. Find how the spaceship velocity modulus increased in the process of braking.

**Q.**Velocity of a particle as a function of time is shown in graph which is a parabola. If slope of the graph at t=0 is 2 units and v=p+qt+rt2, then (Assume SI units everywhere)

- q=4
- r=−0.5
- v0=6 m/s
- Velocity of particle is zero at t=2√3+2 sec

**Q.**A body starts from the origin and moves along the x−axis such that velocity at any instant is given by (4t3−2t) where t is in second and velocity is in m/s. What is the acceleration of the particle, when it is 2m from the origin?

- 28m/s2
- 22m/s2
- 12m/s2
- 10m/s2

**Q.**Velocity of a particle as a function of time is shown in graph which is a parabola. If slope of the graph at t=0 is 2 units and v=p+qt+rt2, then (Assume SI units everywhere)

- q=4
- r=−0.5
- v0=6 m/s
- Velocity of particle is zero at t=2√3+2 sec

**Q.**A body changes direction by an angle a, without changing speed (v). Change in magnitude of velocity is

- zero
- 2v sin a/2
- v sin a/2
- v sin a

**Q.**The position vector of an object at any time t is given by 3t2^i+6t^j+^k. Its velocity along y-axis has the magnitude

- 9
- 6
- 0
- 6 t