Question
Starting from a stationary position, Rahul pedals his
bicycle to attain a velocity of 6 ms⁻¹ in 30 s. Then he applies brakes such that the velocity of the bicycle comes down to 4 ms⁻¹ in the next 5 s. Calculate the acceleration of the bicycle in both the cases.Solution
• For the first case (acceleration while speeding up): o Initial velocity (u) = 0 m/s (stationary) o Final velocity (v) = 6 m/s o Time (t) = 30 s o Acceleration (a) = (v - u) / t = (6 m/s - 0 m/s) / 30 s = 0.2 m/s² • For the second case (deceleration while slowing down): o Initial velocity (u) = 6 m/s o Final velocity (v) = 4 m/s o Time (t) = 5 s o Acceleration (a) = (v - u) / t = (4 m/s - 6 m/s) / 5 s = -0.4 m/s² (negative because it’s deceleration)

If a + b + c = 12 and ab + bc + ca = 47, and a, b, c are real numbers, find the value of a³ + b³ + c³ − 3abc.
If a + `1/b` = 1 and b + `1/c` =1 , then the value of c + `1/a` is

A sum of Rs. 25,000 is invested in SIP 'G' which offers 7% p.a. simple interest for 7 years. The interest received from SIP 'G' is invested in SIP 'H' w...
If
= 2 then find In a best-of-two chess match between Player X and Player Y, the probability that Player X wins a game is (5/9), and the probability that Player Y loses ...
If 10x2 – 6xy+y² – 4x+4= 0, then find the value of (3x+2y).
If x 2 – 15x + 51 = 0, then determine the value of (x – 5) + {1/(x – 5)}.
For a =-4 and b = 5, value of a² – b² is: