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Question: The position of an object moving along x-axis is given by x = a + bt<sup>2</sup>, where a = 8.5 m an...

The position of an object moving along x-axis is given by x = a + bt2, where a = 8.5 m and b = 2.5 m s-2 and t is measured in seconds. The velocity of the object at t = 2 s is

A

5ms−15ms^{- 1}

B

10ms−110ms^{- 1}

C

15ms−115ms^{- 1}

D

20ms−120ms^{- 1}

Answer

10ms−110ms^{- 1}

Explanation

Solution

Here, x=a+bt2x = a + bt^{2}

Where, a=8.5mandb=2.5ms−1a = 8.5mandb = 2.5ms^{- 1}

Velocity, v=dxdt=ddt(a+bt2)=2btv = \frac{dx}{dt} = \frac{d}{dt}(a + bt^{2}) = 2bt

At t = 2s,

v=2(2.5ms−2)(2s)=10ms−1v = 2(2.5ms^{- 2})(2s) = 10ms^{- 1}