A person travelling on a straight line moves with a uniform velocity \({v}_{{1}}\) for some time and with uniform velocity \({v}_{{2}}\) for the next equal time. The average velocity \(v\) is given by( )
A. \({v}=\frac{{{v}_{{1}}+{v}_{{2}}}}{{2}}\)
B. \({v}=\sqrt{{{v}_{{1}}{v}_{{2}}}}\)
C. \(\frac{{2}}{{v}}=\frac{{1}}{{v}_{{1}}}+\frac{{1}}{{v}_{{2}}}\)
D. \(\frac{{1}}{{v}}=\frac{{1}}{{v}_{{1}}}+\frac{{1}}{{v}_{{2}}}\)
Two fat astronauts each of mass 120 kg are travelling in a closed spaceship moving at a sped of 15 km/s in the outer space far remvoed from tall other material objects. The total mass of the spaceship and its contents including the stronauts is 660 kg. If the astronuts do slimming exercise and thereby reduce theri mases to 90 kg, each with wht velocity will spaceship move?
A wheel rotates with a constasnt acceleration of \({2.0}{r}{a}\frac{{d}}{{s}^{{2}}}\). If the wheel starts from rest, how many evolutions wil it make in the first 10 senconds?
The equation of a prticle executing simple harmonic motion is \({x}={\left({5}{m}\right)}{\sin{{\left[{\left(\pi{s}^{{-{{1}}}}\right)}{t}+\frac{\pi}{{3}}\right]}}}.\) Write down the amplitude time period and maximum speed. Also find the velocity at t=1s.
A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens. Find the locations of the two images formed.
A sound source, fixed at the origin, is continuously emitting sound at a frequency of 660 Hz. The sound travels in air at a speed of \({330}{m}{s}^{{-{{1}}}}\). A listener is moving along the line x = 336 m at a constant speed of 26 m Find the frequency of the sound as observed by the listener when he is a. at \({y}=-{140}{m},{b}.{a}{t}{y}={0}{\quad\text{and}\quad}{c}.{a}{t}{y}={140}{m}\).
A sample of ideal gas \({\left(\gamma={1.4}\right)}\) is heated at constant pressure. If an amount 140 J of heat is supplied to the gas, find (a) the changes in internal energy of the gas, (b) the work done by the gas.