Motion in a Straight Line Set-2 MCQ Online Practice Test | Class JEE

Q1. A rubber ball is released from a height of $5 \ \mathrm{m}$ above the floor. It bounces back repeatedly, always rising to $81 / 100$ of the height through which it falls. Find the average speed of the ball. (Take $g = 10 \ \mathrm{ms}^{-2}$ ) [(JEE Main 2021)]

(A)

$2.50 \ \mathrm{ms}^{-1}$

(B)

$3.0 \ \mathrm{ms}^{-1}$

(C)

$2.0 \ \mathrm{ms}^{-1}$

(D)

$3.50 \ \mathrm{ms}^{-1}$

Q2. A car accelerates from rest at a constant rate for some time after which it decelerates at a constant rate to come to rest. If the total time elapsed is $t$ seconds, the total distance travelled is: [(JEE Main 2021)]

(A)

$\frac{\alpha \beta t^2}{\alpha - \beta}$

(B)

$\frac{\alpha \beta t^2}{2 (\alpha - \beta)}$

(C)

$\frac{\alpha \beta t^2}{2 (\alpha + \beta)}$

(D)

$\frac{\alpha \beta t^2}{(\alpha + \beta)}$

Q3. A mosquito is moving with a velocity $\vec{v} = 0.5 t^2 \hat{i} + 3 t \hat{j} \ \mathrm{m/s}$ and accelerating in uniform conditions. What will be the direction of mosquito after $2 \ \mathrm{s}$ ? [(JEE Main 2021)]

(A)

$45^\circ$ from y-axis

(B)

$30^\circ$ from y-axis

(C)

$60^\circ$ from y-axis

(D)

$0^\circ$ from y-axis

Q4. The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta x^2$ , where $\alpha$ and $\beta$ are constants and $x \& y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection and the maximum height attained $H$ are respectively given by: [(JEE Main 2021)]

(A)

$\tan^{-1}(\alpha), \frac{\alpha^2}{4 \beta}$

(B)

$\tan^{-1}(\alpha), \frac{\alpha}{2 \beta}$

(C)

$\tan^{-1}(\sqrt{\alpha}), \frac{\alpha}{4 \beta}$

(D)

$\tan^{-1}(\sqrt{\alpha}), \frac{\alpha^2}{2 \beta}$

Q5. A scooter accelerates from rest for time $t_1$ at constant rate $a_1$ and then retards at constant rate $a_2$ for time $t_2$ and comes to rest. The correct value of $t_1/t_2$ will be : [(JEE Main 2021)]

(A)

$a_1 / a_2$

(B)

$a_1^2 / a_2^2$

(C)

$a_2 / a_1$

(D)

$a_1 / a_2$

Q6. A stone is dropped from the top of a building. When it crosses a point $5 \ \mathrm{m}$ below the top, another stone starts to fall from a point $25 \ \mathrm{m}$ below the top. Both stones reach the bottom of building simultaneously. The height of the building is : [(JEE Main 2021)]

(A)

50 m

(B)

25 m

(C)

45 m

(D)

35 m

Q7. An engine of a train, moving with uniform acceleration, passes the signal-post with velocity $u$ and the last compartment with velocity $v$ . The velocity with which middle point of the train passes the signal post is : [(JEE Main 2021)]

(A)

$\frac{u+v}{2}$

(B)

$\sqrt{u^2 + v^2}$

(C)

$\frac{\sqrt{u^2 + v^2}}{2}$

(D)

$\sqrt{\frac{u^2 + v^2}{2}}$

Q8. A particle moves such that it's position vector is $\vec{r} = A (\cos \omega t \hat{i} + \sin \omega t \hat{j})$ , where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\vec{v}$ and acceleration $\vec{a}$ of the particle.

(A)

$\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed away from the origin.

(B)

$\vec{v}$ and $\vec{a}$ both are perpendicular to $\vec{r}$ .

(C)

$\vec{v}$ and $\vec{a}$ both are parallel to $\vec{r}$ .

(D)

$\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed towards the origin.

Q9. A particle starts from the origin at $t = 0$ with an initial velocity of $\vec{u} = 10 \hat{j} \ \mathrm{cm/s}$ and moves in the $x-y$ plane with a constant acceleration $\vec{a} = (8 \hat{i} + 2 \hat{j}) \ \mathrm{cm/s}^2$ . The $x$ -coordinate of the particle at the instant when its $y$ -coordinate is $32 \ \mathrm{m}$ is $D \ \mathrm{m}$ . The value of $D$ is [Note: Units seem inconsistent in source, solving based on $32 \ \mathrm{m}$ in $\mathrm{cm/s}$ context as given.]

(A)

32

(B)

50

(C)

60

(D)

40

Q10. In a car race on straight road, car A takes a time $t$ less than car B at the finish and passes finishing point with a speed $v$ more than that of car B. Both the cars start from rest and travel with constant acceleration $a_1$ and $a_2$ , respectively. Then $v$ is equal to [JEE Main 2019]

(A)

$\frac{a_1 a_2}{2} t$

(B)

$\frac{2 a_1 a_2}{a_1 + a_2} t$

(C)

$\sqrt{a_1 a_2} t$

(D)

$\frac{a_1 a_2}{2(a_1 + a_2)} t$

Q11. A passenger train of length $60 \ \mathrm{m}$ travels at a speed of $80 \ \mathrm{km/hr}$ . Another freight train of length $120 \ \mathrm{m}$ travels at a speed of $30 \ \mathrm{km/hr}$ . The ratio of times taken by the passenger train to completely cross the freight train when (i) they are moving in same direction and (ii) in the opposite directions is [JEE Main 2019]

(A)

$11/5$

(B)

$5/2$

(C)

$3/2$

(D)

$25/11$

Q12. A particle is moving with a velocity $\vec{v} = K (y \hat{i} + x \hat{j})$ , where K is a constant. The general equation for its path is (JEE Main 2019)

(A)

$y = x^2 + \text{constant}$

(B)

$y^2 = x + \text{constant}$

(C)

$y^2 = x^2 + \text{constant}$

(D)

$x y = \text{constant}$

Q13. The position coordinates of a particle moving in a 3D coordinate system is given by $x = a \cos \omega t$ , $y = a \sin \omega t$ , and $z = a \omega t$ . The speed of the particle is (JEE Main 2019)

(A)

$a \omega \sqrt{2}$

(B)

$a \omega$

(C)

$a^2 \omega$

(D)

$2 a \omega$

Q14. In the cube of side $a$ , as shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be (JEE Main 2019)

(A)

$\frac{1}{2} a (\hat{j} - \hat{i})$

(B)

$\frac{1}{2} a (\hat{i} - \hat{k})$

(C)

$\frac{1}{2} a (\hat{j} - \hat{i})$

(D)

$\frac{1}{2} a (\hat{i} - \hat{j})$

Q15. Two guns A and B can fire bullets at speeds $1 \ \mathrm{km/s}$ and $2 \ \mathrm{km/s}$ respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is (JEE Main 2019)

(A)

$1 : 16$

(B)

$1 : 2$

(C)

$1 : 4$

(D)

$1 : 8$

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