(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

Easy

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

$A$ lift is going up. The variation in the velocity of the lift is given in the graph. What is the height to which the lift takes the passengers? (in $m$)

MediumIIT 1970

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The variation of velocity of a particle moving along a straight line with time is illustrated in the following figure. The distance travelled by the particle in $4 \, s$ is: (in $, m$)

Easy

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Match Column-$I$ with Column-$II$ based on the distance-time $(d-t)$ graphs provided in the image.
$(1)$ Velocity decreases $(a)$ Linear graph (constant slope)
$(2)$ Velocity increases $(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant $(c)$ Concave down graph (decreasing slope)

Easy

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$A$ bird flies for $4 \, s$ with a velocity of $|t - 2| \, m/s$ in a straight line,where $t$ is time in seconds. It covers a distance of ......... $m$.

Medium

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The speed-time graph of a particle moving along a fixed direction is shown in the figure. What is the average speed of the particle over the intervals: $(a)$ $t = 0\; s$ to $10\; s$,and $(b)$ $t = 2\; s$ to $6\; s$?

Medium

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$(1)$ Velocity decreases	$(a)$ Linear graph (constant slope)
$(2)$ Velocity increases	$(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant	$(c)$ Concave down graph (decreasing slope)

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

$A$ lift is going up. The variation in the velocity of the lift is given in the graph. What is the height to which the lift takes the passengers? (in $m$)

The variation of velocity of a particle moving along a straight line with time is illustrated in the following figure. The distance travelled by the particle in $4 \, s$ is: (in $, m$)

Match Column-$I$ with Column-$II$ based on the distance-time $(d-t)$ graphs provided in the image. $(1)$ Velocity decreases$(a)$ Linear graph (constant slope)$(2)$ Velocity increases$(b)$ Concave up graph (increasing slope)$(3)$ Velocity is constant$(c)$ Concave down graph (decreasing slope)

$A$ bird flies for $4 \, s$ with a velocity of $|t - 2| \, m/s$ in a straight line,where $t$ is time in seconds. It covers a distance of ......... $m$.

The speed-time graph of a particle moving along a fixed direction is shown in the figure. What is the average speed of the particle over the intervals: $(a)$ $t = 0\; s$ to $10\; s$,and $(b)$ $t = 2\; s$ to $6\; s$?

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Match Column-$I$ with Column-$II$ based on the distance-time $(d-t)$ graphs provided in the image.
$(1)$ Velocity decreases $(a)$ Linear graph (constant slope)
$(2)$ Velocity increases $(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant $(c)$ Concave down graph (decreasing slope)