Motion in a Straight Line PYQs

The following plots show variation of velocity (v) with time (t) of a ball thrown vertically upward, and falling back. Which of the following plots is/are correct?

When a ruler falls vertically, 5 different persons catch it with different reaction times (g = 9.8 m s⁻²): A. Person A has reaction time 0.20 s B. Person B has reaction time 0.22 s C. Person C has reaction time 0.18 s D. Person D has reaction time 0.19 s E. Person E has reaction time 0.21 s What is the correct order of the distance travelled by the ruler for each person?

In some appropriate units, time $(t)$ and position $(x)$ relation of a moving particle is given by $t = x^2 + x$. The acceleration of the particle is

The velocity (v) – time (t) plot of the motion of a body is shown below. The acceleration (a) – time (t) graph that best suits this motion is:

A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is:

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 m s⁻¹. The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take g = 10 m s⁻²):

The ratio of the distances travelled by a freely falling body in the 1ˢᵗ, 2ⁿᵈ, 3ʳᵈ and 4ᵗʰ seconds is:

The displacement-time graphs of two moving particles make angles of 30° and 45° with the x-axis as shown in the figure. The ratio of their respective velocities is:

A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let Sₙ be the distance travelled by the block in the interval t = n − 1 to t = n. Then, the ratio Sₙ / Sₙ₊₁ is:

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is: (g = 10 m/s²)

A person travelling in a straight line moves with a constant velocity $v_1$ for certain distance $x$ and with a constant velocity $v_2$ for next equal distance. The average velocity $v$ is given by the relation

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\vec{E}$. Due to the force q$\vec{E}$, its velocity increases from 0 to 6 m/s in one second. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are:

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?

A particle covers half of its total distance with speed v₁ and the rest half distance with speed v₂. Its average speed during the complete journey is:

A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, then the percentage error in the estimation of g is

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is $S_1$ and that covered in the first 20 seconds is $S_2$ then:

The distance travelled by a particle starting from rest and moving with an acceleration 4/3 ms⁻² in the third second is

A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms⁻¹ to 20 ms⁻¹ while passing through a distance 135 m in t second. The value of t is

A particle shows distance-time curve as given in the figure. The maximum instantaneous velocity of the particle is around the point

An object is thrown vertically upward with some speed. It crosses two points p, q which are separated by h metre. If tₚ is the time between p and highest point and coming back, and t$_q$ is the time between q and highest point and coming back, relate acceleration due to gravity g, tₚ, t$_q$ and h.

A particle moves along a straight line OX. At a time t (in seconds), the distance x (in metres) of the particle from O is given by x = 40 + 12t − t³. How long would the particle travel before coming to rest?

A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 s for every circular lap. The average velocity and average speed for each circular lap respectively are:

Two bodies, A (of mass 1 kg) and B (of mass 3 kg), are dropped from heights of 16 m and 25 m respectively. The ratio of the time taken by them to reach the ground is:

A ball is thrown vertically upward. It has a speed of $10\,\text{m/s}$ when it has reached one half of its maximum height. How high does the ball rise? (Take $g = 10\,\text{m/s}^2$)