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Standard XII

Physics

Finding Average Velocity

This displace...

Question

This displacement along x-axis are represented by $x = 4 t + 4 t^{2}$ and $y = 5 t$ . the velocity of particle at $t = 1$ second is equal to

4

units

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5

units

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13

units

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9

units

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Solution

The correct option is C $13$ units
Displacement along x-axis,
$x = 4 t + 4 t^{2}$
Velocity, $v_{x} = \frac{d x}{d t} |_{t = 1 s} = 4 + 8 t |_{t = 1 s} = 4 + 8 \times 1 = 12 m / s$
Displacement along y-axis,
$y = 5 t$
$v_{y} = \frac{d y}{d t} = 5 m / s$
The velocity of the particle is
$\to v = {\to v}_{x}^i + \to v^j$
$\to v = 12^i + 5^j$
Magnitude, $| \to v | = \sqrt{12^{2} + 5^{2}} = 13 m / s$
The correct option is C.

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This displacement along x-axis are represented by x=4t+4t2 and y=5t. the velocity of particle at t=1 second is equal to

The correct option is C 13 unitsDisplacement along x-axis,x=4t+4t2Velocity, vx=dxdt|t=1s=4+8t|t=1s=4+8×1=12m/sDisplacement along y-axis,y=5tvy=dydt=5m/sThe velocity of the particle is→v=→vx^i+→v^j→v=12^i+5^jMagnitude, |→v|=√122+52=13m/sThe correct option is C.

This displacement along x-axis are represented by $x = 4 t + 4 t^{2}$ and $y = 5 t$ . the velocity of particle at $t = 1$ second is equal to