# A car moves on a circular path such that its speed is given by $$v= Kt$$, where $$K$$ = constant and $$t$$ is time. Also given: radius of the circular path is $$r$$. The net acceleration of the car at time $$t$$ will be: 1. $$\sqrt{K^{2} +\left(\frac{K^{2} t^{2}}{r}\right)^{2}}$$ 2. $$2K$$ 3. $$K$$ 4. $$\sqrt{K^{2} + K^{2} t^{2}}$$

Subtopic:  Circular Motion |
80%
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Raindrops are falling with speed $$v$$ vertically downwards and a man is running on a horizontal road with speed $$u.$$ The magnitude of the velocity of the raindrops with respect to the man is:
1. $$v-u$$
2. $$v+u$$
3. $$\sqrt{{v}^2 + {u}^2 \over 2}$$
4. $$\sqrt{{v}^2 + {u}^2}$$

Subtopic:  Relative Motion |
82%
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A boy runs on a circular track of radius $$R$$ (in km) with a speed of $$\frac{πR}{2}$$ km/h in the clockwise direction for $$3$$and then with $$πR$$ km/h in the anticlockwise direction for $$1$$ h. The magnitude of his displacement will be:
1. $$\frac{πR}{2}$$
2. $$\frac{R}{\sqrt{2}}$$
3. $$\frac{3πR}{2}$$
4. $$\sqrt{2}R$$

Subtopic:  Position & Displacement |
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The equation of trajectory of a projectile is given by $$y = x-10x^{2}$$Its speed of projection is: ($$g =1 0$$ m/${\mathrm{s}}^{2}$)
1. $$1$$ m/s

2. $$2$$ m/s

3. $$3$$ m/s

4. $$4$$ m/s

Subtopic:  Projectile Motion |
73%
From NCERT
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A body starts moving from rest on a horizontal ground such that the position vector of the body with respect to its starting point is given by $$r= 2 t\hat{i}+3t^2\hat j$$. The equation of the trajectory of the body is:
1. $$y =1.5x$$
2. $$y =0.75x^2$$
3. $$y =1.5x^2$$
4. $$y =0.45x^2$$

Subtopic:  Position & Displacement |
67%
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A particle starts moving with constant acceleration with initial velocity ($$\hat{\mathrm{i}}+5\hat{\mathrm{j}}$$$\stackrel{}{\mathrm{}}$) m/s. After $$4$$ seconds, its velocity becomes ($$3\hat{\mathrm{i}}-2\hat{\mathrm{j}}$$) m/s. The magnitude of its displacement in 4 seconds is:
1. $$5$$ m
2. $$10$$ m
3. $$15$$ m
4. $$20$$ m

Subtopic:  Uniformly Accelerated Motion |
65%
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If a particle is moving in a circular orbit with constant speed, then:

 1 its velocity is variable. 2 its acceleration is variable. 3 its angular momentum is constant. 4 All of the above

Subtopic:  Circular Motion |
78%
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A projectile is projected with initial kinetic energy $$K$$. If it has kinetic energy $$0.25K$$ at its highest point, then the angle of projection is:
1. $$30^{\circ}$$
2. $$45^{\circ}$$
3. $$60^{\circ}$$
4. $$75^{\circ}$$

Subtopic:  Projectile Motion |
67%
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If the position of a particle varies according to the equations $$x= 3t^2$$${}^{}$, $$y =2t$$, and $$z= 4t+4$$, then which of the following is incorrect?

 1 Velocities in $$y$$ and $$z$$ directions are constant 2 Acceleration in the $$x\text-$$direction is non-uniform 3 Acceleration in the $$x\text-$$direction is uniform 4 Motion is not in a straight line
Subtopic:  Acceleration |
75%
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If three coordinates of a particle change according to the equations $$x = 3 t^{2}, y = 2 t , z= 4$$, then the magnitude of the velocity of the particle at time $$t=1$$ second will be:
1. $$2\sqrt{11}~\text{unit}$$
2. $$\sqrt{34}~\text{unit}$$

3. $$40~\text{unit}$$
4. $$2\sqrt{10}~\text{unit}$$

Subtopic:  Speed & Velocity |
81%
From NCERT
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