A car travels in a straight line along a road. Its distance ' x ' from a stop sign is given as a function of ' t ' by the equation x ( t ) = α t + β t 3 , where α = 2 . 0 m s - 1 , β = 0 . 01 m s - 3 . Calculate the average velocity of the car in the time interval t = 2 . 00 sec sec to 4 . 00 sec .

Question

A car travels in a straight line along a road. Its distance ' x ' from a stop sign is given as a function of ' t ' by the equation x ( t ) = α t + β t 3 , where α = 2 . 0 m s - 1 , β = 0 . 01 m s - 3 . Calculate the average velocity of the car in the time interval t = 2 . 00 sec sec to 4 . 00 sec ., 2 . 28 m s - 1, 4 . 94 m s - 1, 3 . 34 m s - 1, 4 . 12 m s - 1

MARKS App · Accepted Answer

The given equation of displacement in the above question, x ( t ) = α t + β t 3 , then the average velocity will be calculated by the idea of change in displacement per unit change in time, v = d x d t = x 4 - x 2 4 - 2 = α t + β t 3 - α t + β t 3 4 - 2 ⇒ v = α 4 + β 4 3 - α 2 + β 2 3 4 - 2 ⇒ v = 2 4 + 0 . 01 4 3 - 2 2 + 0 . 01 2 3 4 - 2 = 2 . 28 m s - 1 Then we have found that the average velocity fo the car is, 2 . 28 m s - 1 .

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