Mock Test 1 — Kinematics

A particle's velocity is $v = 4 + 3t^2$ m/s. The displacement from $t = 0$ to $t = 2$ s is:

A body is projected from ground at $30^\circ$ with speed $20$ m/s. Time of flight ($g = 10 \text{ m/s}^2$):

A particle moves so that $x(t) = 5\sin(2t)$. Maximum velocity:

A ball is dropped from $80$ m. With $g = 10 \text{ m/s}^2$, velocity on impact:

A car traveling at $72$ km/h is brought to rest in $5$ s. Average retardation:

From the top of a $25$ m tower, a stone is projected horizontally with $15$ m/s. Time to reach the ground ($g = 10 \text{ m/s}^2$):

Two trains, $100$ m and $200$ m long, move in opposite directions on parallel tracks at $30$ km/h and $45$ km/h. Time to cross each other:

A particle moves with constant tangential acceleration $a_t = 2 \text{ m/s}^2$ on a circle of radius $2$ m. After how much time will its tangential and centripetal accelerations be equal? (start from rest)

A ball is thrown vertically up with $20$ m/s. After $1$ s, another ball is dropped from $20$ m above the starting point. They will meet at height (above start, $g = 10 \text{ m/s}^2$):

The position of a particle is $\vec{r}(t) = (3t)\hat{i} + (4t - 5t^2)\hat{j}$. Its initial velocity is:

A projectile has range $40$ m and maximum height $10$ m. The angle of projection (in degrees, to nearest integer):

A stone is dropped freely; in the last second it covers $25$ m. The total time of fall (s, $g = 10 \text{ m/s}^2$):

A particle's velocity is $v = 5 - 2t$ (SI). The total distance covered in first $5$ s (in m):

Assertion (A): A projectile launched at $45^\circ$ has maximum range. Reason (R): $\sin 2\theta$ is maximum when $\theta = 45^\circ$.

Assertion (A): In uniform circular motion, velocity is constant. Reason (R): The speed is constant in uniform circular motion.