superman is flying 54.5m/s when he sees a train about to fall into the river 850m away. He must reach the train in 4.22s. What acceleration does he need?
+33614 Use the constant acceleration, kinematic equation s = ut +(1/2)at2 where u = initial velocity, t = time taken, s = distance and a = acceleration.
Rearrange to get: a = 2(s - ut)/t2
a = 2(850 - 54.5*4.22)/4.222 m/s2
$${\mathtt{a}} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{850}}{\mathtt{\,-\,}}{\mathtt{54.5}}{\mathtt{\,\times\,}}{\mathtt{4.22}}\right)}{{{\mathtt{4.22}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{a}} = {\mathtt{69.631\: \!185\: \!283\: \!349\: \!430\: \!6}}$$
acceleration ≈ 69.63 m/s2
.
+33614 Use the constant acceleration, kinematic equation s = ut +(1/2)at2 where u = initial velocity, t = time taken, s = distance and a = acceleration.
Rearrange to get: a = 2(s - ut)/t2
a = 2(850 - 54.5*4.22)/4.222 m/s2
$${\mathtt{a}} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{850}}{\mathtt{\,-\,}}{\mathtt{54.5}}{\mathtt{\,\times\,}}{\mathtt{4.22}}\right)}{{{\mathtt{4.22}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{a}} = {\mathtt{69.631\: \!185\: \!283\: \!349\: \!430\: \!6}}$$
acceleration ≈ 69.63 m/s2
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