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The velocity of a particle moving along a straight line is v=At+Bt², where A and B are constants. The distance travelled by the particle between t=1 s and t=2 s is

Asked in NEET 2016 Phase-I · Integrating a variable acceleration

• (1) (3A)/2+(7B)/3
• (2) A/2+B/3
• (3) (3A)/2+4B
• (4) 3A+7B

Step-by-step solution

Why the other options are wrong

• (2) This is the distance from t=0 to t=1 s, the lower limit alone, with the upper limit never substituted.
• (3) Integrates the At term correctly but treats Bt² as though it integrated to Bt³ without the factor of one third.
• (4) Substitutes t=2 and t=1 into v itself rather than into its integral, so it never divides by the powers at all.

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