Question

Help needed! Physics masters! Class 10! Chapter: Motion Quetsion: A particle with initial velocity u moves with a constant acceleration a for time t. Find: 1) The displacement of the particle in the last 1sec 2) Evaluate it for u=5m/s and a=2m/s2 when t=10sec

Answer 1

Given:

• initial velocity= u
• Acceleration = a
• time taken = t

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Solution:

a)

let the displacemet at last one sec be St

▪The position at time t is

$s = ut + \dfrac{1}{2} a {t}^{2}$

▪The position at time (t-1s) is:

$s1 = u(t - 1) + \dfrac{1}{2} a{(t - 1)}^{2}$

$= ut - u(1s) + \dfrac{1}{2} a {t}^{2} - at(1s) + \dfrac{1}{2} a {(1s)}^{2}$

Thus displacement in last 1sec is:

St= S- S1

=$u(1s) + at(1s) - \dfrac{1}{2} a {(1s)}^{2}$

$\pink{= u(1s) + \dfrac{a}{2} (2t - 1s)(1s)}$ ----- eq i

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(b)

Putting given values in equation 1 we get,

$s = 5( \dfrac{m}{s} )(1s) + \dfrac{1}{2} (2 \frac{m}{ {s}^{2} })(2 \times 10s - 1s)(1s)$

$= 5m + \dfrac{m}{ {s}^{2} } (19s)(1s)$

$= 5 m+ 19m$

$\bold{\red{=24m}}$