$A$ particle has an initial velocity of $(3\hat i + 4\hat j) \; ms^{-1}$ and an acceleration of $(0.4\hat i + 0.3\hat j) \; ms^{-2}$. Its speed after $10 \; s$ is:

The centripetal acceleration of a particle in uniform circular motion is $18 \,m/s^2$. If the radius of the circular path is $50 \,cm$, the change in velocity of the particle in a time of $\frac{\pi}{18} \,s$ is (in $\,m/s$)

$A$ ball is thrown from the ground at an angle $\theta$ with the horizontal and with an initial speed $u_0$. For the resulting projectile motion,the magnitude of the average velocity of the ball up to the point when it hits the ground for the first time is $V_1$. After hitting the ground,the ball rebounds at the same angle $\theta$ but with a reduced speed of $u_0 / \alpha$. Its motion continues for a long time as shown in the figure. If the magnitude of the average velocity of the ball for the entire duration of motion is $0.8 V_1$,the value of $\alpha$ is:

An insect trapped in a circular groove of radius $12 \; cm$ moves along the groove steadily and completes $7$ revolutions in $100 \; s$.
$(a)$ What is the angular speed,and the linear speed of the motion?
$(b)$ Is the acceleration vector a constant vector? What is its magnitude?

$A$ projectile is launched at an angle $\alpha$ with the horizontal with a velocity $20 \; m/s$. After $10 \; s$,its inclination with the horizontal is $\beta$. The value of $\tan \beta$ will be: $(g = 10 \; m/s^2)$

What determines the nature of the path followed by a particle?