Instantaneous Velocity and Speed PYQs: JEE Mains Physics

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1. 1. The velocity (\(v\)) versus time (\(t\)) plot of a particle is shown in the figure, for a time interval of \(40\text{ s}\). The total distance travelled by the particle and the average velocity during this period are, respectively _______.
   2026 Easy
2. 2. The displacement x versus time graph is shown below.
   
   (A) The average velocity during 0 to 3 s is \(10 \mathrm{~m} / \mathrm{s}\)
   (B) The average velocity during 3 to 5 s is \(0 \mathrm{~m} / \mathrm{s}\)
   (C) The instantaneous velocity at \(\mathrm{t}=2 \mathrm{~s}\) is \(5 \mathrm{~m} / \mathrm{s}\)
   (D) The average velocity during 5 to 7 s and instantaneous velocity at \(\mathrm{t}=6.5 \mathrm{~s}\) are equal
   (E) The average velocity from \(t=0\) to \(t=9 \mathrm{~s}\) is zero
   Choose the correct answer from the options given below: 2025 Medium
3. 3. The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is _______ km .
   2025 Easy
4. 4. The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between \(t=0\) to \(t=4 \mathrm{~s}\) ?
   
   2025 Easy
5. 5. Which of the following curves possibly represent one-dimensional motion of a particle?
   
   
   
   
   Choose the correct answer from the options given below : 2025 Medium
6. 6. A particle is moving in a straight line. The variation of position ' \(x\) ' as a function of time ' \(t\) ' is given as \(x=\left(t^3-6 t^2+20 t+15\right) m\). The velocity of the body when its acceleration becomes zero is _______. 2024 Hard
7. 7. A particle is moving in one dimension (along the x-axis) under the action of a variable force. Its position \( x \) (in meters) varies with time \( t \) (in seconds) according to the equation \( x = -3t^3 + 18t^2 + 16t + 16 \). The velocity of the particle when its acceleration becomes zero is _________ \( \text{m/s} \).
   2024 Hard
8. 8. Position of an ant ( \(\mathrm{S}\) in metres) moving in \(\mathrm{Y}-\mathrm{Z}\) plane is given by \(S=2 t^2 \hat{j}+5 \hat{k}\) (where \(t\) is in second). The magnitude and direction of velocity of the ant at \(t=1 \mathrm{~s}\) will be : 2024 Hard
9. 9. From the \(v\) - \(t\) graph shown. the ratio of distance to displacement in \(25\,s\) of motion
   2023 Medium
10. 10. Match Column\(-I\) with Column\(-II :\) Choose the correct answer from the options given below:
    2023 Medium
11. 11. The distance travelled by an object in time \(t\) is given by \(s =(2 \cdot 5) t ^2\). The instantaneous speed of the object at \(t =5\,s\) will be \(....\,ms ^{-1}\) 2023 Easy
12. 12. The position of a particle related to time is given by \(x =\left(5 t ^2-4 t +5\right) m\). The magnitude of velocity of the particle at \(t=2\,s\) will be \(...........ms^{-1}\) 2023 Easy
13. 13. The position-time graphs for two students \(A\) and \(B\) returning from the school to their homes are shown in figure \((A)\) \(A\) lives closer to the school \((B)\) \(B\) lives closer to the school \((C)\) \(A\) takes lesser time to reach home \((D)\) \(A\) travels faster than \(B\) \((E)\) \(B\) travels faster than \(A\) Choose the correct answer from the options given below :
    2023 Medium
14. 14. The velocity time graph of a body moving in a straight line is shown in figure.The ratio of displacement to distance travelled by the body in time \(0\) to \(10\,s\) is
    2023 Medium
15. 15. If \(t =\sqrt{ x }+4\), then \(\left(\frac{ dx }{ dt }\right)_{ t =4}\) is. 2022 Medium
16. 16. Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by \( x_p(t)=at+bt^2 \) and \(x_Q(t)= ft- t^2\). At what time do the cars have the same velocity \(?\)  2022 Medium
17. 17. A car accelerates from rest at a constant rate \(\alpha\) for some time after which it decelerates at a constant rate \(\beta\) to come to rest. If the total time elapsed is \(t\) seconds, the total distance travelled is 2021 Hard
18. 18. The velocity of a particle is \(v = v _{0}+ gt + Ft ^{2}\). Its position is \(x=0\) at \(t=0\); then its displacement after time \(( t =1)\) is : 2021 Easy
19. 19. The speed verses time graph for a particle is shown in the figure. The distance travelled (in \(m\) ) by the particle during the time interval \(t=0\) to \(t=5\, s\) will be
    2020 Easy
20. 20. The velocity \((v)\) and time \((t)\) graph of a body in a straight line motion is shown in the figure. The point \(S\) is at \(4.333\) seconds. The total distance covered by the body in \(6 \;s\) is\(.......m\)
    2020 Medium
21. 21. A particle is moving with speed \(v= b\sqrt x\) along positive \(x-\) axis. Calculate the speed of the particle at time \(t = \tau\) (assume that the particle is at origin at \(t = 0\) ). 2019 Hard
22. 22. A particle starts from the origin at time \(t = 0\) and moves along the positive \(x-\) axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time \(t = 5\,s\) ?.........\(m\)
    2019 Easy
23. 23. The position of a particle as a function of time \(t\), is given by \(x\left( t \right) = at+ b{t^2} - c{t^3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be 2019 Hard
24. 24. A man in a car at location \(Q\) on a straight highway is moving with speed \(v\). He decides to reach a point \(P\) in a field at a distance \(d\) from highway (point \(M\) ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance \(RM\), so that the time taken to reach \(P\) is minimum?
    2018 Hard

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