Question #128866

At the instant shown in Fig. 1, cars A and B are traveling with speeds of 18 m/s and 12 m/s, respectively. Also at this instant, A has a decrease in speed of 2 m/s2, and B has an increase in speed of 3 m/s2

velocity and acceleration of B with respect to A.

velocity and acceleration of B with respect to A.

Expert's answer

Solution

Given data

speed of car A = 18 m/s

speed of car B = 12m/s

we are assuming both cars are moving along +x-axis direction then velocity of car A (V_{A})= +18m/s

velocity of car B (V_{B})=+12 m/s

acceleration of car A (a_{A)}= -2 m/s^2

acceleration of car B (a_{B)}= +3 m/s^2

Now by apply of fomula of relative velocity

V_{BA}=V_{B }-V_{A}

by putting the values of V_{A} and V_{B}

V_{BA}=12-18

V_{BA}= -6 m/s

it mean velocity of B with respect to A is along -X axis direction.

By the formula of relative acceleration of car B with

car A is

a_{BA}=a_{B }- a_{A}

_{ =3 - (-2)}

_{ }a_{BA =5 m/s^2}

it mean acceleration of B with respect to A is along +X axis direction.

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