Starting from a stationary position, Rahul paddles his bicycle to attain a velocity of 6 ms–1 in 30 seconds. Then he applies brakes such that the velocity comes down to 4 ms–1 in the next 5 seconds. Calculate the acceleration of the bicycle in both the cases.

Explanation

According to the question, in the first case Initial velocity ($u$) = 0 Time ($t$) = 30 seconds Final velocity ($v$) = 6 m/s According to the equation of motion $\vec{v} = \vec{u} + \vec{a}t$ $$ 6 = 0 + a \times 30 $$ $$ a = \frac{6}{30} = 0.2 m/sec^2 $$ (470) ## Page 19 In the second situation, the acceleration due to the brake will be defined as decelerating acceleration. according to the equation of motion Initial velocity (u) = 6 m/s Final velocity (v) = 4 m/s Time (t) = 5 seconds according to the equation of motion $$ \vec{v} = \vec{u} + \vec{a}t $$ v = 6 + a × 5 4 = 6 + a × 5 – 2 = a × 5 a = $-\frac{2}{5}$ = -0.4 m/sec² ## Area and Perimeter