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The position of a particle moving on X-a...

The position of a particle moving on X-axis is given by `x =At^(2) + Bt + C` The numerical values of A, B and C are 7, -2 and 5 respectively and SI units are used. Find
(a) The velocity of the particle at t= 5
(b) The acceleration of the particle at t =5
(c ) The average velocity during the interval t = 0 to t = 5
(d) The average acceleration during the interval t = 0 to t = 5

Text Solution

Verified by Experts

`x = 7t^(2) - 2t + 5`
(a) `v = (dx)/(dt) = 14t - 2`
at `t=5, v = 14 xx 5-2 = 68 m//s`
(b) `a= (dv)/(dt) = 14 m//s^(2)`
(c ) Average velocity = `("displacement")/("Time")= (x_5- x_0)/(5-0)`
`x_5 = 7(5)^(2) - 2(5) + 5 = 170 `m
`x_(0) = 7(0)^(2)- 2(0) + 5 = 5`m
`v_("avg") = (170-5)/( 5) = 33 m//s`
(d) Average acceleration
`" " = ("Change in velocity")/("Time interval") = (v_5 - v_0)/( 5-0)`
`v_5 = 14 xx 5- 2 = 68 m//s`
`v_0 = 14 xx 0 -2 = -2m//s`
`a_("avg") = (68-(-2))/(5-0) = 14 m//s^(2)`
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