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Question

The position of the particle is given by x=2t24t+4 in m. The average speed of the particle in 6 sec is

A
436 m/s
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B
263 m/s
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C
273 m/s
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D
233 m/s
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Solution

The correct option is B 263 m/s
As we know that the velocity of the particle as a function of time is given by
dxdt=d(2t24t+4)dt
v=4t4
Now, v(t)=4t4, we will check if the particle has changed its direction or not within the asked time interval, i.e. the time when velocity of the particle becomes zero.
4t4=0 t=1 sec
And, we have x(t)=2t24t+4
So, at t=0,x=4 m,
at t=1,x=2×124×1+4=2 m
at t=6,x=2×624×6+4=52 m
The motion of the particle can be represented as shown

So, the average speed of the particle is 2×2+486=263 m/s

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