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The velocity-time graph of a particle in...

The velocity-time graph of a particle in one-dimensional motion is shown in Fig 3.29:

(a) Which of the following formylae are correct for describing the motion of the particle over the time -interval `t_(1)` to `t_(2)`:
(a) `x(t_(2)) = x(t_(1)) + v (t_(1)) (t_(2) - t_(1)) + (1//2) a (t_(2) - t_(1))^(2)`
(b) `v(t_(2)) = v(t_(1)) + a (t_(2) - t_(1))`
(c) `v_("average") = (x (t_(2)) - x(t_(1)))//(t_(2) - t_(1))`
(d) `a_("average") = (v(t_(2)) - v(t_(1)))//(t_(2) - t_(1))`
(e) `x(t_(2)) = x(t_(1)) + v_("average") (t_(2) - t_(1)) + (1//2) a_("average") (t_(2) - t_(1))^(2)`
(f) `x(t_(2)) - x(t_(1))` = area under the `v - t` curve bounded by the t-axis and the dotted line shown.

Text Solution

Verified by Experts

As the motion of the particle over the interval `t_(1)` and `t_(2)` is non-unifom. Therefore the relation c,d,f are correct but a,b,e represent uniform acceleration.
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