Question

${\large{\red{\underbrace{\green{\boxed{\bf{CHALLANGE \: MODERATORS }}}}}}}$

Starting from a stationary position Rony paddles his bicycle to attain the velocity of 8ms-¹ in 30 s.Than he applies brakes such that the velocity of the bicycle comes down to 4m s-¹ in the next 5 s. Calculate the acceleration of bicycle in both cases.
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Answer 1

Answer:

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Explanation:

$so \: here \\ as \: rony \: starts \: from \: stationary \: point \: which \: is \: at \: rest \: initially \\ its \: initial \: velocity \: must \: be \: 0 \: ie \: u = 0 \\ so \: here \: \\ final \: velocity \: (v) = 8 \: m/s \\ moreover \: time \: taken \: (t) = 30.s \\ so \: we \: know \: that \\ acceleration = \frac{(v - u)}{t} \\ \\ = \frac{(8 - 0)}{30} \\ \\ = \frac{8}{30} \\ \\ = 0.26667 \\ = 0.267 \: m/s {}^{2}$

$so \: in \: second \: case \\ as \: he \: applies \: brakes \: to \: his \: cycle \\ there \: is \: retardation \: ie \: decelaration \: and \: hence \: motion \: of \: paddling \: shoud \: act \: in \: opposite \: direction \: ie \: in \: reverse \: direction \: such \: that \\ acceleration \: ie \: a \: is \: negative \\ \\ so \: here \: final \: velocity \: (v) = 8 \: m/s \\ initial \: velocity \: (u) = 4 \: m/s \\ new \: time \: taken \: = 5.s \\ so \: using \\ acceleration \: = \frac{(v - u)}{t} \\ = \frac{(8 - 4)}{5} \\ = \frac{4}{5} \\ = 0.8 \\ since \: there \: is \: retardation \: \\ a = - 0.8 \: m/s {}^{2}$

Answer 2

Answer:

For first case:

Initial velocity =0

Final velocity =80m/s

Time =30sec

v=u+at

8=0+a×30

8=30a

a= 30/8

a=3.75

For second case:

Initial velocity =8m/s

Final velocity =4m/s

Time taken =5sec

v=u+at

4=8+a×5

4−8=5a−2=5a

a=5/2

a=0.4m/s

2

Explanation:

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