A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.) (a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors \hat{i} and \hat{j}. 1. (Enter in box 1) m/s^2\hat{i}+(Enter in box 2) m/s^2\hat{j} (b) Determine the car's average speed. 3. ( Enter in box 3) m/s (c) Determine its average acceleration during the 33.0-s interval. 4. ( Enter in box 4) m/s^2\hat{i}+ 5. ( Enter in box 5) m/s^2\hat{j}

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.) (a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors \hat{i} and \hat{j}. 1. (Enter in box 1) m/s^2\hat{i}+(Enter in box 2) m/s^2\hat{j} (b) Determine the car's average speed. 3. ( Enter in box 3) m/s (c) Determine its average acceleration during the 33.0-s interval. 4. ( Enter in box 4) m/s^2\hat{i}+ 5. ( Enter in box 5) m/s^2\hat{j}

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asked 2021-04-15
A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 235 m, and the car completes the turn in 33.0 s. (Enter only the answers in the input boxes separately given.)
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors \(\displaystyle\hat{{{i}}}\) and \(\displaystyle\hat{{{j}}}\).
1. (Enter in box 1) \(\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+{\left({E}{n}{t}{e}{r}\in{b}\otimes{2}\right)}{P}{S}{K}\frac{{m}}{{s}^{{2}}}\hat{{{j}}}\)
(b) Determine the car's average speed.
3. ( Enter in box 3) m/s
(c) Determine its average acceleration during the 33.0-s interval.
4. ( Enter in box 4) \(\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{i}}}+\)
5. ( Enter in box 5) \(\displaystyle\frac{{m}}{{s}^{{2}}}\hat{{{j}}}\)

Answers (1)

2021-04-17
here,
distance travelled , d = 235 m
time taken , t = 33 s
speed of car , \(\displaystyle{v}={\frac{{{d}}}{{{t}}}}\)
v = 7.12 m/s
let the radius be r
\(\displaystyle{d}={2}\cdot\pi\cdot{\frac{{{r}}}{{{4}}}}\)
\(\displaystyle{235}={2}\cdot\pi\cdot{\frac{{{r}}}{{{4}}}}\)
PSKr=149.68ZSSK m
centripital accelration, \(\displaystyle{a}={\frac{{{v}^{{2}}}}{{{r}}}}\)
\(\displaystyle{a}={\frac{{{7.12}^{{2}}}}{{{149.68}}}}\)
\(\displaystyle{a}={0.34}\frac{{m}}{{s}^{{2}}}\)
at angle of 35 degree
acceleration of car, \(\displaystyle{a}_{{1}}={\left(-{\cos{{\left({35}\right)}}}{i}+{\sin{{\left({35}\right)}}}\right)}\cdot{a}\)
\(\displaystyle{a}_{{1}}=-{0.27}{i}+{0.19}{j}\)
the acceleration when the car is at B located at an angle of 35.0 is \(\displaystyle{\left(-{0.27}{i}\ \frac{{m}}{{s}^{{2}}}+{0.19}{j}\ \frac{{m}}{{s}^{{2}}}\right)}\)
(b) the car average speed is v
the car average speed is 7.12\ m/s
c) initial speed of car, \(\displaystyle{u}_{{1}}={7.12}{i}\ \frac{{m}}{{s}}\)
final speed of car, \(\displaystyle{v}_{{1}}={7.12}{j}\ \frac{{m}}{{s}}\)
average acceleration \(\displaystyle={\frac{{{\left({v}_{{1}}-{u}_{{1}}\right)}}}{{{t}}}}\)
average acceleration \(\displaystyle={\frac{{{7.12}{j}-{7.12}{i}}}{{{33}}}}\)
average acceleration \(\displaystyle={\left(-{0.22}{i}\ \frac{{m}}{{s}^{{2}}}+{0.22}{j}\ \frac{{m}}{{s}^{{2}}}\right)}\)
the average acceleration during the 33.0-s interval is \(\displaystyle{\left(-{0.22}{i}\ \frac{{m}}{{s}^{{2}}}+{0.22}{j}\ \frac{{m}}{{s}^{{2}}}\right)}\)
0

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