362259
If the velocity of a particle is \(v = At + B{t^2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1 \, s\) and \(2 \, s\) is
362261
The position \(x\) of a particle w.r.t. time \(t\) along \(x\)-axis is given by \(x = 9{t^2} - {t^3},\) where \(x\) is in metre and \(t\) in sec. What will be the position of this particle when it achieves maximum speed along the \( + x\) direction?
1 \(32\,m\)
2 \(54\,m\)
3 \(81\,m\)
4 \(24\,m\)
Explanation:
Given, the position \(x\) of a particle w.r.t. time \(t\) along \(x\)- axis \(x = 9{t^2} - {t^3}\) \(v = \frac{{dx}}{{dt}} = \frac{d}{{dt}}\;(9{t^2} - {t^3})\) \(v = 18t - 3{t^2}\) \(a = \frac{{dv}}{{dt}} = \frac{d}{{dt}}(18t - 3{t^2})\) \(a = 18 - 6t\) When speed of particle is maximum, its acceleration is zero, i.e., \(a = 0 \Rightarrow t = 3s\) Putting in Eq. (1), we obtain position of particle at the time \(x = 9{(3)^2} - {(3)^3} = 81 - 27 = 54\,m\)
PHXI03:MOTION IN A STRAIGHT LINE
362262
Which of the following is a one dimensional motion?
362259
If the velocity of a particle is \(v = At + B{t^2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1 \, s\) and \(2 \, s\) is
362261
The position \(x\) of a particle w.r.t. time \(t\) along \(x\)-axis is given by \(x = 9{t^2} - {t^3},\) where \(x\) is in metre and \(t\) in sec. What will be the position of this particle when it achieves maximum speed along the \( + x\) direction?
1 \(32\,m\)
2 \(54\,m\)
3 \(81\,m\)
4 \(24\,m\)
Explanation:
Given, the position \(x\) of a particle w.r.t. time \(t\) along \(x\)- axis \(x = 9{t^2} - {t^3}\) \(v = \frac{{dx}}{{dt}} = \frac{d}{{dt}}\;(9{t^2} - {t^3})\) \(v = 18t - 3{t^2}\) \(a = \frac{{dv}}{{dt}} = \frac{d}{{dt}}(18t - 3{t^2})\) \(a = 18 - 6t\) When speed of particle is maximum, its acceleration is zero, i.e., \(a = 0 \Rightarrow t = 3s\) Putting in Eq. (1), we obtain position of particle at the time \(x = 9{(3)^2} - {(3)^3} = 81 - 27 = 54\,m\)
PHXI03:MOTION IN A STRAIGHT LINE
362262
Which of the following is a one dimensional motion?
362259
If the velocity of a particle is \(v = At + B{t^2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1 \, s\) and \(2 \, s\) is
362261
The position \(x\) of a particle w.r.t. time \(t\) along \(x\)-axis is given by \(x = 9{t^2} - {t^3},\) where \(x\) is in metre and \(t\) in sec. What will be the position of this particle when it achieves maximum speed along the \( + x\) direction?
1 \(32\,m\)
2 \(54\,m\)
3 \(81\,m\)
4 \(24\,m\)
Explanation:
Given, the position \(x\) of a particle w.r.t. time \(t\) along \(x\)- axis \(x = 9{t^2} - {t^3}\) \(v = \frac{{dx}}{{dt}} = \frac{d}{{dt}}\;(9{t^2} - {t^3})\) \(v = 18t - 3{t^2}\) \(a = \frac{{dv}}{{dt}} = \frac{d}{{dt}}(18t - 3{t^2})\) \(a = 18 - 6t\) When speed of particle is maximum, its acceleration is zero, i.e., \(a = 0 \Rightarrow t = 3s\) Putting in Eq. (1), we obtain position of particle at the time \(x = 9{(3)^2} - {(3)^3} = 81 - 27 = 54\,m\)
PHXI03:MOTION IN A STRAIGHT LINE
362262
Which of the following is a one dimensional motion?
362259
If the velocity of a particle is \(v = At + B{t^2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1 \, s\) and \(2 \, s\) is
362261
The position \(x\) of a particle w.r.t. time \(t\) along \(x\)-axis is given by \(x = 9{t^2} - {t^3},\) where \(x\) is in metre and \(t\) in sec. What will be the position of this particle when it achieves maximum speed along the \( + x\) direction?
1 \(32\,m\)
2 \(54\,m\)
3 \(81\,m\)
4 \(24\,m\)
Explanation:
Given, the position \(x\) of a particle w.r.t. time \(t\) along \(x\)- axis \(x = 9{t^2} - {t^3}\) \(v = \frac{{dx}}{{dt}} = \frac{d}{{dt}}\;(9{t^2} - {t^3})\) \(v = 18t - 3{t^2}\) \(a = \frac{{dv}}{{dt}} = \frac{d}{{dt}}(18t - 3{t^2})\) \(a = 18 - 6t\) When speed of particle is maximum, its acceleration is zero, i.e., \(a = 0 \Rightarrow t = 3s\) Putting in Eq. (1), we obtain position of particle at the time \(x = 9{(3)^2} - {(3)^3} = 81 - 27 = 54\,m\)
PHXI03:MOTION IN A STRAIGHT LINE
362262
Which of the following is a one dimensional motion?
