iran-konkur

2024 konkur-riazi_1403_ordibehesht_specialized

5 maths questions

43-- A football with mass $45\,\text{g}$ is shot from a penalty spot at a speed of $20\,\dfrac{\text{m}}{\text{s}}$ toward the goal and hits the goalkeeper at a speed of $16\,\dfrac{\text{m}}{\text{s}}$. What is the total work done on the ball?
(1) $-10$ (2) $-16.2$ (3) $-32.4$ (4) $-64.8$
Q44 Constant acceleration (SUVAT) Velocity-time or acceleration-time graph interpretation View
44-- The position--time graph of a particle moving along the $x$-axis with constant acceleration is shown below. What is the magnitude of the average speed of the particle in the first 7 seconds?
\begin{minipage}{0.45\textwidth} [Figure: position-time graph with x(m) axis showing value 24 at top, curve passing through origin, reaching a minimum near t=2, then rising to 24 at t=7; t(s) axis shows values 2 and 7] \end{minipage} \begin{minipage}{0.45\textwidth} (1) $\dfrac{25}{8}$
(2) $\dfrac{25}{7}$
(3) $\dfrac{23}{8}$
(4) $\dfrac{23}{7}$ \end{minipage}
Q45 Variable acceleration (1D) Find displacement/position by integrating velocity View
45-- The position--time equation of a particle in SI units is $x = 2t^2 - 12t + 8$, at moment $t = 0$. How many seconds after $t = 0$ is the particle's distance from the origin less than or equal to 8 meters?
(1) $2$ (2) $3$ (3) $4$ (4) $6$
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Q46 Constant acceleration (SUVAT) Velocity-time or acceleration-time graph interpretation View
46. The figure below shows the acceleration–time graph of a moving object that at moment $t = 0\,\text{s}$ has velocity $\vec{V} = +\!\left(8\,\dfrac{\text{m}}{\text{s}}\right)\hat{i}$ and has been moving. What is the average velocity of the object in these 8 seconds (in meters per second)?
[Figure: acceleration-time graph with $a\,(\frac{\text{m}}{\text{s}^2})$ on vertical axis and $t\,(\text{s})$ on horizontal axis. The graph shows $a = +2$ from $t=0$ to $t=3$, then $a = -6$ from $t=3$ to $t=8$.]
  • [(1)] $12$
  • [(2)] $15$
  • [(3)] $\dfrac{43}{4}$
  • [(4)] $\dfrac{53}{6}$

Q47 Constant acceleration (SUVAT) Distance in successive equal time intervals View
47. An object at moment $t = 0\,\text{s}$ starts moving from rest with constant acceleration. The displacement of this object in the $n$-th second is how many times the displacement in the second $n$ equals the displacement in the second two?
$$\frac{5}{3} \quad (1) \qquad \frac{9}{4} \quad (2) \qquad \frac{3}{2} \quad (3) \qquad 2n \quad (4)$$