List of top Mathematics Questions on Mechanics

A particle is moving in a straight line such that its distance at any time \(t\) is given by \[ s=\frac{t^4}{4}-2t^3+4t^2+7, \] then its acceleration is minimum at \[ t=\_ \]

Two cars A and B start from the same point and travel the same distance. The ratio of their speeds is 3: 4. Car A takes 30 minutes more than car B to complete the journey. If car B takes 't' minutes, then what is the value of 't' (in minutes)?

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a} + \vec{b}| = 15$ and
\( \vec{a} \times (3\hat{i} - 4\hat{j} + 5\hat{k}) = (3\hat{i} - 4\hat{j} + 5\hat{k}) \times \vec{b} \)
What is the value of $|(\vec{a} + \vec{b}) \cdot (2\hat{i} + 3\hat{j} + \hat{k})|$?

If two stones are thrown vertically upwards with their velocities in the ratio 2:5, then the ratio of the maximum heights attained by the stones is

If three forces of magnitudes 8 newtons, 5 newtons and 4 newtons acting a point are in equilibrium, then the angle between the two smaller forces is

Two forces acting at a point of a body are equilibrium if and only if they
(A) are equal in magnitude
(B) have same direction
(C) have opposite direction
(D) act along the same straight line
(E) are not equal in magnitude but have same direction
Choose the correct answer from the options given below:

Match List-I with List-II

\[ \begin{array}{|l|l|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; P \text{ and } Q \text{ are two perpendicular forces, acting at a point} & (I) \; R = |P - Q| \\ (B) \; P \text{ and } Q \text{ are equal, forces acting at a point at an angle } \alpha & (II) \; R = P + Q \\ (C) \; P \text{ and } Q \text{ are acting at a point in same direction} & (III) \; R = 2P \cos(\tfrac{\alpha}{2}) \\ (D) \; P \text{ and } Q \text{ are acting at a point in opposite direction} & (IV) \; R = \sqrt{P^2 + Q^2} \\ \hline \end{array} \]
Choose the correct answer from the options given below: