Home
Class 12
PHYSICS
Check the correctness of the formula S =...

Check the correctness of the formula `S = ut + 1/3 "at"^2` where S is the distance , u is velocity , a is acceleration and t is time.

Text Solution

Verified by Experts

Dimensionally , LHS = [L]
`RHS = [LT^(-1)][T[LT^(-2)][T]^(2) = [L] + [L] = [L]`
Since , the dimension of each term on both sides are same, the given equation is dimensionally correctly.
Promotional Banner

Topper's Solved these Questions

  • UNITS AND MEASUREMENT

    AAKASH SERIES|Exercise EXERCISE - I|156 Videos

  • UNITS AND MEASUREMENT

    AAKASH SERIES|Exercise EXERCISE - II|61 Videos

  • SEMICONDUCTOR DEVICES

    AAKASH SERIES|Exercise EXERCISE - III|3 Videos

  • UNITS AND MEASUREMENTS

    AAKASH SERIES|Exercise EXERCISE -3|66 Videos

Similar Questions

Explore conceptually related problems

Chek the correctness of the relation, S_(nth) = u +(a)/(2)(2n -1), where u is initial velocity, a is acceleratin and S_(nth) is the distance travelled by the body in nth second.

Check the correctness of following equation by the method of dimensions : S=ut+(1)/(2)at^(2) . where S is the distance covered bu a body in time t, having initial velocity u and acceleration a.

Check the correctness of the equations (i) s=ut+1/2at^(2) (ii) v^(2)=u^(2)+2as using dimensions.

A particle starts rotating from rest according to the formula theta = (t^(2)//64) - (t//8) " where " theta is the angle in radian and t in s . Find the angular velocity and angular acceleration at the end of 4 s .

The motion of a particle along a straight line is described by the function x=(2t -3)^2, where x is in metres and t is in seconds. Find (a) the position, velocity and acceleration at t=2 s. (b) the velocity of the particle at origin.

The motion of a particle along a straight line is described by the function x=(2t -3)^2, where x is in metres and t is in seconds. Find (a) the position, velocity and acceleration at t=2 s. (b) the velocity of the particle at origin.

(a) Write a equation of motion in different states and derive the relation : s=u+(1)/(2)a(2t-1) Where, s is the distance covered in t^("th") second, u is initial velocity and a is uniform acceleration.

The distance travelled by a particle in n^(th) second is S_n =u+a/2 (2n-1) where u is the velocity and a is the acceleration. The equation is

Figure is a graph of the coordinate of a spider crawling along the x-axis. (a) Fraph tis velocity and acceleration as functionsof time. (b) In a motion diagram, show the position, velocity, and acceleration of the spider at the five times: t=2.5 s , t=10 s, t=20 s, t=30 s , .

A car is running on a straight road . The distance travelled and time taken are connected by the formula = t^(2) -2t where t is measured in hours and s in km. When the odometer reading is 15, what is the speedometer reading ? [ Odometer measures s and the speedmeter measures velocity]

AAKASH SERIES-UNITS AND MEASUREMENT-PRACTICE EXERCISE
  1. Check the correctness of the formula S = ut + 1/3 "at"^2 where S is th...

    Text Solution

    |

  2. The ratio of S.I unit of the C.G.S unit of gravitational constant 'G' ...

    Text Solution

    |

  3. If units in two systems of measurments are in the ratio 2 : 3, the rat...

    Text Solution

    |

  4. If the unit of length is 4 m and that of velocity is 6 ms^(-1) , the u...

    Text Solution

    |

  5. If the unit of force is 1N, the unit of work done is 10 J and the unit...

    Text Solution

    |

  6. If the unit of length , mass and time each be doubled , the unit of wo...

    Text Solution

    |

  7. A new unit of length is chosen such that the speed of light is vacuum ...

    Text Solution

    |

  8. In planetary motion the areal velocity of position vector of a planet ...

    Text Solution

    |

  9. If pressure P, velocity V and Time T are taken as fundamental physical...

    Text Solution

    |

  10. The reverberation period T of a room on its volume V, its surface area...

    Text Solution

    |

  11. If the vibration frequency of atoms in a crystaal depends on the atomi...

    Text Solution

    |

  12. The time period of a soap bubble is T which depneds on pressure p dens...

    Text Solution

    |

  13. The method of dimensional analysis can be used to derive which of the ...

    Text Solution

    |

  14. If the velocity is represented by V, force by F and work by W . These ...

    Text Solution

    |

  15. If C the velocity of light, h planck's constant and G Gravitational co...

    Text Solution

    |

  16. If m is the mass of drop of a liquid of radius 'r' then (mg)/(pi r) ha...

    Text Solution

    |

  17. The dimensionally correct formula is

    Text Solution

    |

  18. The expression S = a/b (1 - e^(-bt)) is dimensionally true. The dimens...

    Text Solution

    |

  19. According to Bernoullis theoram p/d + (v^2)/2 + gh = constant, dimensi...

    Text Solution

    |

  20. If R is the electric resistance and C is the capacitance, the dimensio...

    Text Solution

    |

  21. Velocity of sound in a medium is given by A^(1//2) d^(-1//2), where 'd...

    Text Solution

    |