Two cars A and B initially at rest are moving in the same direction with accelerations, a_1 and a_2 respectively. After a certain time, they achieve…

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Two cars A and B initially at rest are moving in the same direction with accelerations, a_1 and a_2 respectively. After a certain time, they achieve velocities v_1 and v_2 respectively and are separated by a distance of 50 m. If a_1-a_2=4 m s^(-2), then the quantity v_1-v_2 will be

MARKS Content Team · Accepted Answer

Correct answer: (B) 20 m s^(-1). Use the first equation of motion, v=u+at, both the cars are initially at rest it means the equations for two different cars moving with difference acceleration after same time, v_1=0+a_1t & v_2=0+a_2t⇒v_1-v_2=a_1-a_2t ...1 , now the use the second equation of motion, s_1-s_2=1/2a_1t^2-1/2a_2t^2⇒t^2=(2s_1-s_2)/(a_1-a_2)⇒v1-v22s1-s2^2=2s_1-s_2⇒v_1-v_2=√(2s_1-s_2a_1-a_2)⇒v_1-v_2=√(2×50×4)=20 m s^(-1)

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Two cars A and B initially at rest are moving in the same direction with accelerations, a1 and a2 respectively. After a certain time, they achieve velocities v1 and v2 respectively and are separated by a distance of 50 m. If a1-a2=4 m s-2, then the quantity v1-v2 will be

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