The equation of motion of a particle is given | vedclass

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(B) Given the equation of motion: $s(t) = at^2 + bt + c$. Velocity $v(t) = \frac{ds}{dt} = 2at + b$. Acceleration $a_{acc}(t) = \frac{dv}{dt} = 2a$. G

Vedclass · Accepted Answer

$a + c = b$

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(B) Given the equation of motion: $s(t) = at^2 + bt + c$. Velocity $v(t) = \frac{ds}{dt} = 2at + b$. Acceleration $a_{acc}(t) = \frac{dv}{dt} = 2a$. Given acceleration is $10 \ m/s^2$,so $2a = 10 \implies a = 5$. Given velocity after $2 \ s$ is $30 \ m/s$: $v(2) = 2a(2) + b = 30 \implies 4a + b = 30$. Substituting $a = 5$: $4(5) + b = 30 \implies 20 + b = 30 \implies b = 10$. Given displacement after $1 \ s$ is $20 \ m$: $s(1) = a(1)^2 + b(1) + c = 20 \implies a + b + c = 20$. Substituting $a = 5$ and $b = 10$: $5 + 10 + c = 20 \implies 15 + c = 20 \implies c = 5$. Now check the options: $a + c = 5 + 5 = 10$. Since $b = 10$,we have $a + c = b$.

The equation of motion of a particle is given by $s = at^2 + bt + c$. If the displacement after $1 \ s$ is $20 \ m$,the velocity after $2 \ s$ is $30 \ m/s$,and the acceleration is $10 \ m/s^2$,then which of the following is true?

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