A particle starts with an initial velocity and passes successively over the two halves of a given distance with constant accelerations `a_1 and a_2` respectively. Show that the final velocity is the same as if the whole distance is covered with a uniform acceleration `(a_1 + a_2)/2 .`

If same force is acting on two masses m_1 and m_2 and the accelerations of two bodies are a_1 and a_2 respectively, then

Starting from rest a particle is first accelerated for time t_1 with constant acceleration a_1 and then stops in time t_2 with constant retardation a_2. Let v_1 be the average velocity in this case and s_1 the total displacement. In the second case it is accelerating for the same time t_1 with constant acceleration 2a_1 and come to rest with constant retardation a_2 in time t_3. If v_2 is the average velocity in this case and s_2 the total displacement, then

Starting from rest a particle is first accelerated for time t_1 with constant acceleration a_1 and then stops in time t_2 with constant retardation a_2. Let v_1 be the average velocity in this case and s_1 the total displacement. In the second case it is accelerating for the same time t_1 with constant acceleration 2a_1 and come to rest with constant retardation a_2 in time t_3. If v_2 is the average velocity in this case and s_2 the total displacement, then

Starting from rest a particle is first accelerated for time t_1 with constant acceleration a_1 and then stops in time t_2 with constant retardation a_2. Let v_1 be the average velocity in this case and s_1 the total displacement. In the second case it is accelerating for the same time t_1 with constant acceleration 2a_1 and come to rest with constant retardation a_2 in time t_3. If v_2 is the average velocity in this case and s_2 the total displacement, then

A body starts from rest & moves with constant acceleration a_1 for time t_1 then it retards uniformly with a_2 , in time t_2 and finally comes at rest. Find (t_1)/(t_2)

A body A starts from rest with an acceleration a_1 . After 2 s another body B starts from rest with an acceleration ar If they travel equal distance in the 5th second after the start of A. a_1 : a_2 is equal to

A body A starts from rest with an acceleration a_1 . After 2 seconds, another body B starts from rest with an acceleration a_2 . If they travel equal distances in the 5th second, after the start of A , then the ratio a_1 : a_2 is equal to :

A body A starts from the rest with an acceleration a_1 . After 2 second another body B starts from rest with an acceleration a_2 . If they travel equal distance in the 5th second after the start of A, then what will be the ratio a_1 : a_2 .