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 Obtain equations of motion for constant acceleration, using method of calculus.
A car is moving along a straight line, say OP in fig 3.11. It moves from O to P in 18 s and return from P to Q in 6.0 s. What are the average velocity and average speed of the car in going (a) from O to P and (b) from O to P and back to Q ?
“The distances traversed, during equal intervals o time, by a body falling from rest, stand to one another in the same rate as the odd numbers beginning with unity [namely, 1:3:5:7…..]”. Prove it.
The position of an object moving along x-axis is given by x = a+ bt2 where a = 8.5 m, b = 2.5 m s-2 and t is measured in seconds. What is its velocity as t = 0 s and t = 0.2 s. What is the average velocity between t = 2.0 s and t = 4.0 s?
 A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ m0 of a particle in term of its speed v and the speed of light, c [ This relation first arose as a consequence of special relativity due to Albert Einstein]. A boy recalls the relation almost correctly but forgets where to put the constant c. He writes: m= m_0/〖(1- v^2)〗^(1/2)
A book with many error contains four different formulas for the displacement y of a parties undergoing a certain periodic motion : (a) y = a sin 2π t/T (b) y = a sin vt (c)  y = (a/T) sin t/a (d) y = (a √2 (sin 2π t/T + cos 2π t/T) (a = maximum displacement of the particle, v = speed of the particle, T = time-period of motion), Rule out the wrong formulas on dimensional grounds.
A physical quantity P is related to four observables a, b, c and das follows: P = a3b 2 / √(c  ) d The percentage error of measurement in a, b, c and d are 1% 3% 4% and 2%, respectively. What is the percentage error in the quantity p? If the value of p calculated using the above relation turns out to be 3.763, to what value should you around off the result?