Answer :
I. [tex]\( x_1 = t^3 \)[/tex]
- Velocity [tex](\( v \)): \( v = 3t^2 \)[/tex]
- Acceleration [tex](\( a \)): \( a = 6t \)[/tex]
- At [tex]\( t = 2 \)[/tex] sec:
- [tex]\( v = 3 \times 2^2 = 12 \) units/s[/tex]
- \[tex]( a = 6 \times 2 = 12 \) units/s²[/tex]
II. [tex]\( x = 4t^2 + 2t \)[/tex]
- Velocity [tex](\( v \)): \( v = 8t + 2 \) (differentiate with respect to \( t \))[/tex]
- Acceleration [tex](\( a \)): \( a = 8 \) (constant, as the derivative of \( v \) is a constant)[/tex]
At [tex]\( t = 1 \)[/tex] sec:
-[tex]\( v = 8 \times 1 + 2 = 10 \) units/s[/tex]
- [tex]\( a = 8 \) units/s²[/tex]
III. [tex]\( y = 4 \sin x \)[/tex]
- Velocity[tex](\( v \)): \( v = 4 \cos x \) (differentiate with respect to \( x \))[/tex]
- Acceleration [tex](\( a \)): \( a = -4 \sin x \) (differentiate \( v \) with respect to \( x \))[/tex]
IV. [tex]\( 4 = x^2 - 1 \)[/tex]
- Not clear if you are looking for velocity and acceleration. Please clarify.
V. [tex]\( y = 4 \ln x \)[/tex]
- Velocity[tex](\( v \)): \( v = \frac{4}{x} \) (differentiate with respect to \( x \))[/tex]
- Acceleration [tex](\( a \)): \( a = -\frac{4}{x^2} \) (differentiate \( v \) with respect to \( x \))[/tex]
VI.[tex]\( y = Ax^2 + Bx + C \)[/tex]
- Velocity[tex](\( v \)): \( v = 2Ax + B \) (differentiate with respect to \( x \))[/tex]
- Acceleration [tex](\( a \)): \( a = 2A \) (constant, as the derivative of \( v \) is a constant)[/tex]
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Answers & Comments
Answer :
I. [tex]\( x_1 = t^3 \)[/tex]
- Velocity [tex](\( v \)): \( v = 3t^2 \)[/tex]
- Acceleration [tex](\( a \)): \( a = 6t \)[/tex]
- At [tex]\( t = 2 \)[/tex] sec:
- [tex]\( v = 3 \times 2^2 = 12 \) units/s[/tex]
- \[tex]( a = 6 \times 2 = 12 \) units/s²[/tex]
II. [tex]\( x = 4t^2 + 2t \)[/tex]
- Velocity [tex](\( v \)): \( v = 8t + 2 \) (differentiate with respect to \( t \))[/tex]
- Acceleration [tex](\( a \)): \( a = 8 \) (constant, as the derivative of \( v \) is a constant)[/tex]
At [tex]\( t = 1 \)[/tex] sec:
-[tex]\( v = 8 \times 1 + 2 = 10 \) units/s[/tex]
- [tex]\( a = 8 \) units/s²[/tex]
III. [tex]\( y = 4 \sin x \)[/tex]
- Velocity[tex](\( v \)): \( v = 4 \cos x \) (differentiate with respect to \( x \))[/tex]
- Acceleration [tex](\( a \)): \( a = -4 \sin x \) (differentiate \( v \) with respect to \( x \))[/tex]
IV. [tex]\( 4 = x^2 - 1 \)[/tex]
- Not clear if you are looking for velocity and acceleration. Please clarify.
V. [tex]\( y = 4 \ln x \)[/tex]
- Velocity[tex](\( v \)): \( v = \frac{4}{x} \) (differentiate with respect to \( x \))[/tex]
- Acceleration [tex](\( a \)): \( a = -\frac{4}{x^2} \) (differentiate \( v \) with respect to \( x \))[/tex]
VI.[tex]\( y = Ax^2 + Bx + C \)[/tex]
- Velocity[tex](\( v \)): \( v = 2Ax + B \) (differentiate with respect to \( x \))[/tex]
- Acceleration [tex](\( a \)): \( a = 2A \) (constant, as the derivative of \( v \) is a constant)[/tex]
Question:-
➦ (xii) x = 4t² + 2t find v and at t = 1 sec.
Correct answer:-
➦ Refer to the below mentioned attachment...!!! :)
Thnkuuu...!!! :)
hope it helps...!!! ♡
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