(C) The velocity $v$ is the time derivative of the position $x$ with respect to time $t$.Given $x = a + b t^{2}$.$v = \frac{dx}{dt} = \frac{d}{dt}(a +

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$0 \; m s^{-1}, 10 \; m s^{-1}$

(C) The velocity $v$ is the time derivative of the position $x$ with respect to time $t$.Given $x = a + b t^{2}$.$v = \frac{dx}{dt} = \frac{d}{dt}(a + b t^{2}) = 0 + 2bt = 2bt$.Substituting the given value $b = 2.5 \; m s^{-2}$:$v = 2 \times 2.5 \times t = 5.0 t \; m s^{-1}$.At $t = 0 \; s$,$v = 5.0 \times 0 = 0 \; m s^{-1}$.At $t = 2.0 \; s$,$v = 5.0 \times 2.0 = 10 \; m s^{-1}$.

Class 11 Physics Motion in Straight Line Instantaneous Velocity and Speed and Velocity-time Graph

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The position of an object moving along the $x$-axis is given by $x = a + b t^{2}$,where $a = 8.5 \; m$,$b = 2.5 \; m s^{-2}$,and $t$ is measured in seconds. What is the velocity at $t = 0 \; s$ and $t = 2.0 \; s$?

A
$10 \; m s^{-1}, 20 \; m s^{-1}$
B
$0 \; m s^{-1}, 20 \; m s^{-1}$
C
$0 \; m s^{-1}, 10 \; m s^{-1}$
D
$0 \; m s^{-1}, 0 \; m s^{-1}$

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Motion in Straight Line

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Instantaneous Velocity and Speed and Velocity-time Graph

The acceleration-time graph of a body is shown. The corresponding velocity-time graph of the same body is

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Can the position-time graph of a moving object be parallel to the position axis? Why?

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$A$ body starts from rest and travels a distance $S$ with uniform acceleration,then moves uniformly a distance $2S$ and finally comes to rest after moving further $3S$ under uniform retardation. The ratio of the average velocity to maximum velocity is

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The $v-t$ plot of a moving object is shown in the figure. The average velocity of the object during the first $10$ seconds is...........$m/s$.

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During which time interval is the particle described by these position graphs at rest?

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The position of an object moving along the $x$-axis is given by $x = a + b t^{2}$,where $a = 8.5 \; m$,$b = 2.5 \; m s^{-2}$,and $t$ is measured in seconds. What is the velocity at $t = 0 \; s$ and $t = 2.0 \; s$?

Similar Questions

The acceleration-time graph of a body is shown. The corresponding velocity-time graph of the same body is

Can the position-time graph of a moving object be parallel to the position axis? Why?

$A$ body starts from rest and travels a distance $S$ with uniform acceleration,then moves uniformly a distance $2S$ and finally comes to rest after moving further $3S$ under uniform retardation. The ratio of the average velocity to maximum velocity is

The $v-t$ plot of a moving object is shown in the figure. The average velocity of the object during the first $10$ seconds is...........$m/s$.

During which time interval is the particle described by these position graphs at rest?

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